No, it is not technically possible. Synchronous callouts in Triggers are not allowed. There is an Idea to have Salesforce do this, but it's already a decade old, and may never be implemented. The main concern about callouts during triggers is that it will significantly increase database contention, which may cause deadlocks as the database has to hold record locks for potentially up to 2 minutes, and/or resource exhaustion if too many callouts happened at once.
As a comment from salesforce.com says:
This is something that we can't offer without jeopardizing our
service. If you're in a trigger, you have a database connection open.
If you make a callout, and that callout endpoint is hung, your
connection is hung. That's one connection that your fellow
multi-tenants cannot use. If your trigger is hit by a few hundred
users, our service is blocked.
This is the reason why we do not allow DML in a method prior to making
a callout, even in asynchronous context.
If we were to impose very aggressive timeouts on callouts to reduce
the impact of the above scenario, we'd only make programmers
frustrated with the too-tight limits, and I don't know that we'd add
much to service protection.
Alternative solutions include creating a Flow, and having users enter data through the Flow, which can then callout and verify the data before creating a new record, using a Visualforce page or Lightning component to collect and validate the data, or performing the callout asynchronously and later just showing an error somehow on the record after it's created.
