Does it possible to use Full text search functions like
match() against() with Drupal 8 database Api's OR any alternative to make it work?
No. If you look at the internal
Condition::match() function that's used when building conditional statements with the
condition() method, you can see the list of operators does not include the
AGAINST() operators. The cost of having a DB abstraction layer that supports different DBMS, is you can only support the greatest common feature among them; these operators are MySQL/Postgres specific.
In order to utilize these feature of your database, you'll need to use the
Connection::query() method to perform the query directly.