Wage as little war as possible.
Find a spot on the ocean with a lot of different resources near it. Settle one or two cities near there. Hopefully your capital, but you might spawn on an inland sea without knowing.
Trade with all the Civs.
Buy all the CS.
Win diplomatically.
Portugal is obviously designed to ignore city states. Why would you pay money for a CS when you get their luxury resource for free after Navigation?
I had fun doing the following:
Go Commerce for -25% rushbuy costs combined with Order's level 1 tenet -33% costs for buildings.
Focus on getting to Astronomy quickly, upgrade 4-5 triremes to Naus, use them to explore the whole map in just a few turns. Beeline Industrialization, rushbuy three factories with money from Naus and start Order. Settle new cities on good spots on other continents and rushbuy workshops and aqueducts to get them going. Counter happiness issues with other Order tenets like +2 happiness per monument. Also have enough workers ready to build Feitorias quickly.
A Liberty start makes it easier to build those colonies although you should focus on a rather small empire with big coastal cities in the early game. I'd suggest to ignore religion and focus on trade routes instead. Always have one trade route dedicated to food trades.
If you have multiple good spots at the coast, you might also wanna spend two policies in the exploration tree for early happiness boosts from lighthouses and harbors. Or finish commerce for +2 happiness per luxury.
Victory types:
Cultural - Portugal has a huge advantage when it comes to finding dig sites for artifacts. The Nau is an amazing scout. Colonies can have enough museums to support archeologist spam. Either rushbuy those buildings or spend two policies in the Aesthetics tree for cheaper museums. Finishing the exploration tree for hidden artifacts might also be a good plan.
Science - Rushbuy science buildings asap, +25% science per factory, rationalism
Domination - works well when AI has mostly coastal capitals, Autocracy might be better here for rushbuying an army instead of useless buildings
Diplomatic - no, it's a waste of their ability