Define Victory?
The Egyptians and Syrians attacked simultaneously, the Egyptians crossing the Suez canal and carrying out a brilliant surprise attack on the Bar-Lev Line, pushing forward and securing a defensive perimeter on the eastern side of the Suez canal, nowhere more than 10 miles deep from the canal. For the Egyptians this secured the extent of their war aims; they wanted to secure the Suez Canal and prove that their army could seize and hold ground prior to entering into negotiations. At no time did the Egyptian Command intend to drive across the Sinai and destroy Israel; they were far more realistic of their capabilities and set their sights to more moderate targets.
In the north the Syrians attacked across the Golan Heights cease fire line with the intention of recovering the ground they’d lost in the 1967 Six Day War. They employed a greater density of artillery than the Russians had in their final drive towards Berlin in World War Two! The Syrian attack consisted of 5 divisions and 188 artillery batteries, the Israeli defence consisted of two brigades and 11 artillery batteries. Not only did they attack with an (in theory) overwhelming numerical advantage, they did it on Yom Kippur, when Israeli forces were at their weakest, troops scattered all over the country celebrating the holiest day on the Jewish calendar; the Syrian Command had anticipated that this would mean they would have at least 24 hours before the Israeli reserves started to be deployed, sufficient time to secure their objectives and dig in. In reality the first reserves started arriving in under an hour and the Israelis threw everything they had into the Golan, judging rightly that the Sinai had enough depth to it that even if the Egyptians continued their advance it would take them time to reach anywhere significant and pose a real threat.
The result was that even though they were fighting on two fronts, the Israelis only had to fight one front at a time; destroying one Arab army before turning their attention to the other.
When he Syrians were hard pressed they asked the Egyptians to resume the offensive in the hope that this would take the pressure off them in the north; it didn’t, all it did was simultaneously over extend the Egyptians and expose them to air Israeli air attacks without the protection of Egypt’s static air defences. Consequently when Syria went down, Egypt followed.
In all likelihood the Egyptians would not have been able to hold back the Israelis even if they’d remained dug in close to the Canal; they had a long, static defensive line which the Israelis could attack in concentrated force wherever they chose. But they certainly could have put up a stronger fight or made a fighting withdraw back to the canal.