You can partially mitigate it by making sure DMARC, DKIM, and SPF are configured right. There are tools online you can use to verify they're setup right, don't remember which sites though.
I have used mxtoolbox.com in the past. However, I don't know how reputed they are.
Note that the 'big mail providers' won't accept your mails even after you apply every known trick in the book. This is especially true for the two biggest ones that provide free services and hosted services on customers domains.
Note that the 'big mail providers' won't accept your mails even after you apply every known trick in the book. This is especially true for the two biggest ones that provide free services and hosted services on customers domains.