How important is work experience in first landing a job? (Coming from someone who was originally planning on dental school)

Hey fellows. My question is this, for someone like myself with no full-time work experience and an MS in Finance (Let's say from OSU - Ohio State University), how hard would it be to secure an entry level role in a corporate finance role? I'm basically sitting on two acceptances at this point, one for dental school, and the other for this MS in finance program. My only work experience is pretty pathetic, I've been working a little over 3 years since graduating in 2015 as a math tutor (part time). Originally I was planning on going straight to dental school and foolishly thought that as long as I finish dental school I'll have a job easily enough (which is still true). But I've been having second thoughts on dentistry as a whole, given the absurd levels the debt has reached. My school will cost 400k or more upon graduation . Would it be a good move to enter this MSF program from OSU (which has pretty solid employment stats it seems) even though I have no full time experience? Honestly it feels like finance aligns better with my character since I enjoy working with data and math in general. Truthfully a large part of me went after dentistry fort he wrong reasons (money,prestige,etc.)

I'm 25 right now, 26 later this year
approx 3.7 gpa from Fordham University (undergrad)
Biology major
3+ years work as a part time tutor since 2016