Can I remove the default clock without rooting my phone? I have a modern Pixel Android phone on the most up to date version of Android.

I'd like to not show the time on the homescreen and the topbar.

I've seen many solutions that include rooting the phone.

Is it possible to get rid of these two clocks without rooting the device?
You can use adb to do this without root (But you need a PC). First download Android platform tools from https://developer.android.com/studio/releases/platform-tools now unzip them in a folder in your PC. 

Go to that folder and open Command Prompt. Now in your phone, find the build number and tap it 7-8 times to enable Developer Options. Now open Developer Options and enable USB debugging. Then plug your phone with your PC. Confirm the box.

Now first type adb devices. Then enter the command adb shell to start adb shell. Now type the command pm list packages | grep "clock" or if you have problem with grep then use pm list packages | find "clock". Find the package name of default clock. Now use pm uninstall -k --user 0 package-name. If you see Success message, then clock app will be removed.