Finishing third year here. Going into general practice with a hospital system. I started reaching out to most hospital systems in my area late second year. Your best approach is to leverage connections in these systems. You can email their physician recruiters with your CV and interest but I got back several "we're not looking" emails. It makes a lot of difference if you have a physician friend/colleague speaking up on your behalf. Ultimately, that push got my foot in the door for the interviews.
I would agree that right now is not the best time, but your prime time for interviews is still probably 6 months away. However, if your institution has a travel ban in place (now or in the fall), that would really complicate this. Right now, my institution places everyone on unpaid leave for 14 days of quarantine if they leave the state right now. If travel opens up over the summer and you have places of interest willing to bring you in, I would try to get some of those done while you can.