Recover

If contacts were synced with Google they will restore when you resync. Your emails may still be on the server, depending on how you set the account up. Similarly, do you have any cloud backup of you photos (Flickr, Google Photos, etc)? Stuff like that might even have been set up by default if you have the accounts, so it's worth checking.

But if you have no backup I'm afraid the answer is "you don't". Modern Androids talk to computers over an MTP connection, which doesn't give the computer the sort of filesystem access needed to run file recovery. If the data were on a removable sd card then this would be easy (stick the card in a card reader and run your favourite file recovery software), but of that lot only photos are likely to have been on a removable card (if you have one).