How can we send the logs through REST API without using the Universal forwarder on the application server or any sources
the best way to do this is the Splunk HTTP Event Collector. It's a HTTP(S) API, that you can send your events to.
There is a lot to be considered for this, but the documents explain it pretty well. Check this:
Set up and use HTTP Event Collector in Splunk Web
Introduction to Splunk HTTP Event Collector
Hope that helps - if it does I'd be happy if you would upvote/accept this answer, so others could profit from it. 🙂