How to use unique incremental integer for user ID?

Question

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I'm making a mobile chat app

I heard about load balancing and scalability, to make it able to be used properly by multiple people at different locations of the world at same time

I'm currently hosting the (PostgreSQL) DB and doing tests locally

Here is my concern -> I imagine 2 persons from different continents creating an account at the exact same time

Currently I generate uuid for user ID

But I would like instead to use unique incremental integer, so it would be easier to store and remember for the user

But is it a good idea? Would it be achievable properly without risking to mess up everything?

Could you please give me some hints?

Regards