The only thing you can do without the need for KYC is that you can send a few dollars into the exchange and trade a few coins on the spot market, but once it comes to withdrawal, I don't think you can withdraw without KYC, and even if you can, just like you said, it can't be more than a few dollars.
This is the silly part of this exchanges, they will allow you send as much as you want into their exchange with the knowledge that you cannot withdraw that much and issue no warning during the process, until it comes to withdrawal then you are hit with a pop up warning that you need to pass KYC to be able to withdraw said amount.
As bold as they make minimum withdrawals, they should also put maximum withdrawals for each verification tier.
What I said was you can view these traders without trading on the platform -- some leave contact details (phone, email, even site or TG) and you can usually enquire outside. That's how I found my current main p2p traders.
Some exchange still allow this and some P2P traders still require you to include your number into the chat before the trade starts so they can reach you after making payment.
- Jay -