I had this come up recently for a new client I was setting up a new Google Ad Campaign for. They had a Squarespace site and naturally, we wanted to track form submissions as a conversion in the Google Ad Campaign.
You can create a separate 'thank you' page and have the form redirect to that page after submission. You then track pageviews for this 'thank you' page as a conversion using the Google Ad Conversion Tag or setting up a Google Analytics Goal then importing that into Google Ads to track as a conversion. This is perfectly fine and it's a fairly normal setup.
If for whatever reason the client doesn't want them sent to a 'thank you' page. You can track clicks on the form button as a conversion as well. It's pretty easy to set this up using Google Tag Manager.
I actually just wrote a post about this recently, check it out over here!
I go more in-depth showing you how to set it up with Google Tag Manager and the new Google Analytics 4. After you have that setup, you can simply import that GA Goal into Google Ads to track as a conversion.
The process for setting it up for Universal Google Analytics or Google Ads Conversion Tag is similar. Perhaps I'll write something up on that here soon.
Update: More recently, I've been doing this type of setup for tracking form submissions as a Google Ad conversion.
Next, learn my system for optimizing a Google Ad Campaign to increase conversions and lower your cost per conversion.