Originally Posted by Marshal

Usually no problems with Namecheap, it pretty much takes a minute to change DNS settings. DNS cache on Google's side could be causing the problems.

I would suggest you to contacting Namecheap support or to try using the dig tool to make sure all DNS settings are fine.
https://toolbox.googleapps.com/apps/dig/
https://www.digwebinterface.com/
It's also very useful to register new domains with preset name servers. I don't know does Namecheap still support this.

An alternative to this is to contact Google support and ask them to do the manual verification, if still possible.

There's also another thing called DNS cache and depending on your expiry settings, or the settings on the ISP side (in this case Google side), it could take a while for DNS changes to propagate. Unless there's some technical error on the Namecheap side, I'm pretty much sure it's the default DNS expiry times that you used and Google picked them up and will not try to get fresh results until the DNS cache expires.

Here's more information about how DNS works:
https://en.wikipedia.org/wiki/Domain_Name_System

Hope that was helpful.