Are there "Introductory flights" available to see if I want to pursue training?
Well, to put it bluntly, somebody has to pay for the airplane.  Much like a car, somebody has to pay for the gas and maintenance.  The major difference is that both cost a lot more on an airplane so it is a lot harder to get someone else to pay for it.

However, similar to a car, if you have a friend that owns an airplane they may take you up for a ride and even (legally) let you fly it, but they remain the person in charge and responsible for the safe outcome of the flight.  If you want to try it for free this is probably one of the only ways to do it.

If you are willing to pay for a one-time flight which does not commit you to pay for your entire license, then you can go to almost any place that teaches people how to fly and they will be happy to let you fly with an instructor and charge you only for the time in the airplane and the time with the instructor.  Often they have an "introductory" flight just for this purpose which is discounted for potential students.  This is a relatively small cost in comparison to learning to fly that I highly recommend to anyone before they commit to getting their license.