First: I love the fact that you want a POD with one of my all time favorite female rulers of history (and I've been on an Egyptian history kick lately, so double hurray). That being said: a ship from Egypt traveling to China at this time sounds pretty extreme. King Hatshepsut did send expeditions out, such as one to the legendary land of Punt, which is believed to be somewhere around modern Ethiopia/Somalia. Remember the Nile was just called The River in Egyptian because to them, it was the only body of water that counted, and most of their sailing was up and down this river, especially to Kush. If they wanted to go farther inland than the river went, I believe the boats were made in such a way that the sailors could easily deconstruct them and carry them with them to the next body of water (someone correct me if I'm wrong, remembering back to some podcasts I heard back in January).
The point being that these ships were not made to be great ocean liners, but rather to take advantage of the Nile's nature currents, and to be lightweight enough to move on land if necessary, hardly the vessel you'd need to get all the way to China at this point in history.
However, if we go with the idea of China being an eventual contact rather than immediate one, and want to start leaning in that direction so that Egypt eventually gets there, we could start by establishing an Egyptian colonial presence in Punt. Now, as I understand it, that would be a serious change in mindset for the Egyptians, as Punt and Kush were places that you went and visited/raided rather than settled in. Even the territory her successor Thutmose III gains in the Middle East is really more of military garrison/mining operation rather than a true colony where Egyptians would go and settle and become residents. Egyptians believed in living by the Nile, and definitely believed that the only way to achieve a good afterlife was for your corpse to be returned home (which puts a damper on the pioneer spirit).
So we have to come up with something that causes a major change/upheaval for Egyptian society to adopt the idea of invading and actually inhabiting a territory outside the traditional two Kingdoms. We also have to refocus attention away from the Middle East and Kadesh (in modern Syria) and down toward Kush (Nubia) and eastern Africa. We know that Hatshepsut's original expedition to Punt was overseen by a court official in her ninth year of reign. After that she pivoted back to Lebanon and the Sinai. So what stops that pivot and keeps her more focused on the Horn of Africa? Or at least gets a colony of some kind going there, even if officially she keeps doing her thing back home?
We know that her chief minister Senenmut drops out of the historical record after a certain point, despite enjoying very privileged access to the court and getting to build a tomb close to his king, and also that his body was not found in said elaborate tomb (though whether that came about due to later grave robbers is unknown). We also know he was the tutor of Hatshepsut's daughter Neferure, a position he seems to have valued higher than many of his other more distinguished titles based on his clear affection for this girl, portraying her in statutory almost as his own daughter in an uncle/fatherly role.
Just to be clear because Egyptian genealogies get confusing: Hatshepsut is the daughter of King Thutmose I, third king of the 18th dynasty (the first after overthrowing the Hyksos), and the wife of her half-brother Thutmose II (incest being a common practice of Egyptian royalty: and you thought the Habsburg were inbred). He died young, leaving Hathsepsut as ruling regent for the two-year-old heir Thutomse III, her stepson born to a secondary wife. Neferure was the only child born to Hatshepsut, a daughter of Thutmose II and half-sister of Thutmose III. It's speculated she may have eventually married him and given him a child, but we're not sure, and she may have died during her mother's reign.
Now, some scholars have speculated that Hatshepsut may have been positioning her daughter to succeed her instead of her stepson, as Neferure had an expanded role in the Egyptian court compared to previous royal daughters and also appears to have served as the God's Wife of Amun, the same position Hatshepsut served prior to taking the throne. For the sake of this TL, let's say Hatshepsut did want her daughter to become pharaoh after her, creating a new dynastic line over her stepson/nephew. In the year of the Punt expedition Thutmose III is 12 (not quite old enough to rule yet); we're not sure exactly when Neferure was born, but for the sake of convenience let's say she's roughly similar in age to him (Hatshepsut and her own brother-husband were only three years difference in age).
Let's move forward in time to Year 16 of Hatshepsut's reign; Thutmose III is now 19 and probably getting anxious to "take the reign" (sorry, bad pun). Again, he may have married his half-sister at this point, but for the sake of this TL let's say Hathsepsut is keeping them apart and pushing for her girl to be seen as the next leader. Year 16 is a big one for Hatshepsut because she celebrated her kingly Sed festival, traditionally held after 30 years of rule. She seems to have bent the rules a bit and dated back 30 years to the death of her father, claiming she was his chosen heir and the real power in the land during Thutmose II's time. The Sed festival was a celebration of the king's right to rule as god on earth, a display of physical process and spiritual rebirth. It cemented the king's place as absolute ruler. It sounds like a good time to position her daughter Neferure as the next king.
Now, Hathsepsut was a savvy lady, so I don't think she's going to just wholesale announce a new succession and have a potential uprising on her hands. Instead, she might use the Sed Festival to announce that as god on earth, the living Horus, she's going to make Egypt even greater in her next "30 years." After ceremonially being crowned again with the symbols of Upper and Lower Egypt, let's say she announces that Egypt is going to expand to the farther reaches of the world, cementing god's rule, you get the idea (lots of drinking and partying going on here, people are in a good mood for power slogans). She tells everyone that Thutmose III will play his role as a commander of the army in Kadesh and their northern territory. Lots of cheers, maybe a ceremonial handing over of a whip to him, it's a big moment. Then, as everyone's pumped, she tells them that she will send another expedition to Punt, bigger, better than before, and establish a permanent base to bring back riches to the homeland. Again, lots of cheers, more celebrations. Then, almost as an afterthought, she finishes by saying that her emissary to lead and guide this new mission will be the God's Wife, the child of Horus, Neferure, with her old tutor Senenmut going too as the King's administrator. By this point Senenmut had become one of the most powerful men in the land; sending him sends a clear signal this trip is big time, and he serves as a male figure to be seen as the real power there. But it also shows clear signs of Hathsepsut setting up the same power structure in Punt as she's enjoyed in Egypt: Senenmut as the chief officla, Neferure as a miniature pharaoh. It's far away, so not a threat to the "real" heir yet, but it sets a precedent.
Much as I love the idea of Neferure eventually becoming pharoah herself and Egypt becoming a matriarchy, that's not really our goal, and I think it's a major hurdle to cross, and definitely impossible without getting rid of Thutmose III (which seems unlikely outside of a huge butterfly hitting him on the head, he was a major military leader and tactician). Instead, let's say the colony in Punt thrives, sending a steady stream of tribute back to Egypt, enriching people, and leading to more settlement of merchants and others outside of the military down into Kush and toward Punt, expanding the concept of Egypt. Eventually Neferure returns to Egypt, not as pharoah, but as wife of her half-brother; since we're in an ATL, let's just say she's the mother of his heir Amenemhat (there's some debate there in OTL as to his mother), and the dynasty continues apace with his death and the ascension of his half-brother Amenhotep II.
But the Punt legacy has grown: Senenmut on his death is buried there instead of his original planned tomb back in proper Egypt, which may in part be due to the sea change that happened when Thutmose III took over after Hathsepsut's death. Neferure, as one of her last recorded acts, goes to bury her old tutor, bringing with her elements from his original tomb work back home, and establishes a grand chapel and mortuary cult for him. Other Egyptians in the area also built tombs there, and so rather than establish a new dynasty, Punt establishes a funery practices: an Egyptian can now be buried outside of the traditional two lands, even if at first it is traditional to still have your tomb prepared and built back in the homeland and traveled down the Nile to your new dwelling, those soaking in the spiritual richness on its trip. Once Egyptians are no longer bound by the one River to establish their life after death, we can finally start moving in the direction of longer voyages and farther trading posts.