New list imported and getting high bounce rate

[theGreaseShop]

I imported a customer list of about 8300 names from when we had a similar store on another platform. We just reopened it on Shopify and imported the list. Initially I sent a welcome back email to the whole list and got a bounce rate of 147 names before it quit and failed. Days later I tried a second mailing knowing Shopify automatically does not resend to bounced recipients. I got a bounced rate of 448 on this second mailing. On a third I got 148 bounces. It looks like it will take many months yo screen out all the bounced customers considering there are over 8300 names in the list. Is there any way to better handle this so I can clean the list and start mailing to every valid one. Basically I want to reach all currently valid names on my old customer list that I added to Shopify.