That makes it a bit difficult, since there is definitely a bit of a difference between playing games on a graphics card on older settings, and not being able to play games at all.
That will mean you will want to buy a CPU with decent integrated graphics, so a decent pairing with a 3060 ti would be a 5600g, which is releasing next week. Depending on it's performance, your budget, and it's ability to play the games you want for a few months on integrated graphics, you might be fine.
Otherwise, you are in a bit of a tough spot. You should probably get a cheap old graphics card which can play the games you like for a bit and then upgrade to the graphics card you want.