Implementing Coin-Addresses in internet sites?

Hey there,

not sure if this the right forum but no forum fully relates to this question I have.

So,
this goes out to people who have experience and knowledge about Website-Programming and implementing Coin-Addresses on a site.
I´ve got no clue about Website-Programming but since years, since I got in touch with Bitcoin related sites

I was wondering how Coin-Exchanges or other sites i.e., faucetbox or coinsforcall, markets in the DarkNet (sometimes even with changing to new addresses within seconds),etc. can automatically create Bitcoin (or other coins) addresses for each user/account.

So I´m curious how is it possible to implement Coin-Addresses for depositing and/or withdrawing coins on any site? I was thinking about it a long time but it can´t be the answer to create hundreds (or thousands) of addresses manually and relate them to an user´s account then. There must be an automatic solution somehow. This can´t be done all only fully manually.

If anyone with the needed knowledge or even a site to which my problem belongs to reads this and would give me an answer would be truly appreciated - as said I´m wondering about it since years and now I want to finally get an answer for that.

Thanks a lot and all my best!