I worked at an insurance agency for 12 yrs until very recently.
DON'T TRY TO CLEAN IT YOURSELF. You'll track it everywhere & make everything worse.
Call your insurance agent right away. It's covered subject to deductible.
They will send someone like ServiceMaster or ServePro out. A restoration company....and your home will be sparkling clean when done.
Or if you prefer, call them yourself......but be prepared for $$$$$.
I would file the claim in a heartbeat. Assuming you haven't filed 1 or more claims already in the past 3 yrs. This is a large claim -- I would file no matter what. If next type of claim is small, eat it yourself.
ETA: I had a customer have one right before Christmas once....dust was even on the christmas tree ornaments. She was in tears because she was hosting Christmas. She called later to say how happy she was with how it was all cleaned up. She had another puffback a couple of years later.... I think she just wanted her house cleaned again.

just kidding.
So, look on the bright side...... your spring cleaning will be all done for you!

good luck