Check fuel filter and line for clogging.
Are you running an air box?
You are correct, covering the air inlet of the carb richens the mixture. It’s like choke. Choking the air.
If you haven’t used new gaskets, I’d check for leaks by getting it running (with your thumb) then spraying something (WD40, starting fluid, carb cleaner,…) in the spots where it might be leaking. The RPMs should change if the fluid finds its way into a leak. Might raise rpm, might lower, but it’s the change in rpm you are listening for.
An engine will run lean if there is too much air or not enough fuel. An engine will run rich if there is too much fuel or not enough air.
Running with no air box, more air, leaner
Covering carb with thumb, less air, richer
Air leak, more air, leaner.
clogged carb, fuel line, filter, less fuel, leaner
Oh ya, lastly…
Did you put gas in the tank?