Can I get an eGPU without a thunderbolt 3?

Thunderbolt 3 is not strictly required for an eGPU to work. The people that sell and support them will tell you Thunderbolt 3 is required because if used with Thunderbolt 2 it might not perform as quickly as expected. To connect a Thunderbolt 3 device to a Thunderbolt 2 computer will require a Thunderbolt 2 to Thunderbolt 3 adapter. I have done this to connect a Thunderbolt 3 dock to a Thunderbolt 2 Mac and it works as intended, but the data throughput is limited to that of the Thunderbolt 2. The Thunderbolt 3 adapter makes a physical connection possible, it doesn’t make the connection faster.

Connecting a Thunderbolt device to a USB port is not likely to work. There’s a protocol difference that would take drivers to fix, and I doubt anyone is going to write drivers. Thunderbolt 2 and Thunderbolt 3 are essentially the same protocol so no special drivers needed, but Thunderbolt 2 is going to be half the speed of Thunderbolt 3. Depending on the application and expectations using Thunderbolt 2 may work.

The issue of Apple silicon Macs not supporting eGPUs is also a matter of drivers. There’s no inherent reason any eGPU can’t work with Apple silicon, it is just that nobody has written drivers yet. I’ve seen on Linus Tech Tips where they experimented with an Ethernet based eGPU and got that to work with Apple silicon Macs. Why an Ethernet connection to an eGPU works but not one by Thunderbolt gets complicated really quick. I’m a bit surprised it worked but after some thought I can see why it does.

A Thunderbolt 3 based eGPU should work fine on Thunderbolt 2 with an adapter, for some definition of “fine”. If I’m mistaken on your model of MacBook having a Thunderbolt port then that’s not an option. Ethernet based eGPUs are an option if the software supports that, and like with Thunderbolt 2 vs. Thunderbolt 3 there’s going to be a performance bottleneck because Ethernet isn’t as big of a data pipe. There’s really no easy way around the speed limits of the ports out of the computer, but you should be able to get the computer to talk to a GPU. If this is worth the effort vs. just getting a new computer is up to you.