Hi and Welcome. My Name is ***** ***** I look forward to assisting you today with your question.
I'm sorry about your phone. Unfortunately No. You can't remotely activate the sync option on it. But if you have setup Google account or Samsung account on it, then the contacts and also other data should be still saved on the Google or Samsung server.
Did you check Google Contatcs ? Go here and do you see your contatcs --> https://contacts.google.com/
Let me know how it goes.