Windows recently crashed and I had to do a fresh install. My games were on another hard drive and I've been able to sync the games with the new GOG Galaxy install but when I open the game, it doesn't have my saves. It acts as though it's the first time I've opened the game. It even reset the 'time played' that was displaying. I'm fairly certain my saves are either on my computer or saved in the cloud. How can I get the new GOG Galaxy to recognize the saves?

I hope that makes sense. Thanks for any help.

Go to the Extras tab for the game in question and download the cloud saves backup from there. Compare with your local save folder. If the latter is empty, then place the saves from the cloud backup there. If you don't know where your local save folder is, look up the game on PCGamingWiki.

If the cloud saves backup is empty, use a web browser to check out what's in there:
https://www.gog.com/account/cloud-saves/page/1