I've been wondering; with the seafaring capabilities of, for example, the Genoese, Venetians, etc., how far could Europeans have sailed in the late 1200s? 1300s? Could a European adventurer, for whatever reason, have sailed to China earlier than the Portuguese did OTL?
I mean, I realise that at this time the Silk Road was open for business and European traders could do their work via Constantinople, but for argument's sake let's just assume otherwise. Could a journey south via the Cape of Good Hope have been successful before the Portuguese did it?
Ship building was making huge advances at about that time. Going around the Cape is not for the timid, even in 1500s ships.
Without a PoD that massively improves shipbuilding earlier, your best bet is likely to have the Crusader States hold on (ha, ha, I know) and hold a significant port on the Arabian sea or the Red Sea. Then have them engage in seasonal (monsoon based) trade in the Indian Ocean, and then from a base in India, expand east, setting up another base near Singapore, and from THERE head north to China.
If they managed all this, OTL's Indonesia might end up partly Christian, as, IIRC, the Arabs were only reaching there about the same time.
Even so, you probably don't get to China until ~1250 or 1300.
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On further research, conversion to Islam was only starting to happen by then, although traders had been there for a while.
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On further thought, yet, a long lasting Crusader polity is only going to work if it engages the locals, and ceases to be purely 'European'. By the time you get to India, Singapore, and then China, the traders arriving in China may self-identify as 'Ferengi' and be Roman Catholic, but there won't be hardly anyone a Brit or a German (say) would call 'European'.
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I'm using 'Singapore' as a convenient shorthand for a trade port in the Straits area, whether it be on a small island, in Sumatra or the Malaya peninsula.
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Sigh. Just noticed the OP called for a 'European Power' to reach China. Oops. Ah. OK, maybe Venice takes over the trade route, in exchange for military supplies for said Crusader state? ???