Can a Salesforce trigger call a batch class in Salesforce?

Yes we can invoke. But make sure you are not crossing the governing limits.

The current limit for concurrent batch jobs is 5.

https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_gov_limits.htm

Hi,

You can call a batch from a trigger, but you need to be aware of potential limits you could hit.

You can only have 5 batch jobs queued or executing at once. If your trigger calls batch jobs each time, then you could quickly exceed that limit.

Hope this helps!