Can I implement search box in a prominent app bar, trying to follow Material Design?

I am designing an app with a custom app bar, which in the main screen is a prominent one, meaning it's wider than the usual one. I already have some custom features there, for example city filter. I am wondering, how I could implement a search box in there.

I attach 2 screens. Is it even ok to do something like this? It somehow bothers me, but at the same time I'm having hard time figuring anything else out.

I could also open the search box under the search icon, where there is city filter and the date sort. Would it be any better?

Do you have any other ideas?