Hello, and welcome to TASVideos!
There's a few emulator pages for running MAME games for the purposes for TASing:
There's a lot of resources and support out there for working with LibTAS if you're willing to take the time for setup. Those can also apply to MAME TASing and lets you immediately work with whatever versions of MAME you need in case of regressions and such.
For something in the future that's really promising, there's a MAMEHawk core being worked on for TASing arcade games in the multi-system emulator BizHawk. It's still experimental right now but will be in BizHawk 2.9 when that releases to try it out. Since it would be in BizHawk that means there are a number of tutorials for using BizHawk that can help.
Once you got an emulator set up, the easiest way to get a handle on TASing anything is simply to jump in. Always be willing to ask questions on the forums and the TASVideos Discord if you have questions.