DNS Propagation can be a big challenge while migrating to different hosting or switching to different email providers. In order to make sure there’s as little downtime as possible, the DNS changes should be planned way in advance (24-48 hours ahead of scheduled change). One of the tricks to get the DNS updates across the globe as fast as possible is to reduce the TTL to as low as your service provider allows so that the global DNS servers have the TTL set up accordingly.
Also, after the required DNS change(s) is made, you can submit a request to clear caches from some of the following providers.
Google https://dns.google/cache
Cloudflare https://1.1.1.1/purge-cache/
OpenDNS https://cachecheck.opendns.com/