Google Domains redirecting website

I bought a domain using Google Domains (let’s call it newdomain.com). I also own olddomain.com (bought via register.com) which is hosted on a dedicated server I’m paying for.

I bought newdomain.com from Google so as to take advantage of the email functionality. I would however like to point newdomain.com to the olddomain.com server so that I can create a new site there.

Is there any way I can do this without losing Google’s email functionality?

I’ve tried using the redirection function, but this is a simple redirection, meaning that anybody typing in newdomain.com will actually see olddomain.com in the URL bar while I want them to keep seeing newdomain.com.

Is there a solution to this?