I have a Trek Speed concept series 7 frame size XS triathlon bike which is fitted with 650 size wheels. However I was wondering if I could at all put 700 wheels/tyres on, as when I brought it 2nd hand from the owner they said "Trek only produce XS Frame with 650 wheels otherwise impossible to produce correct geoemtry" and was wondering upon the accuracy of that statement, and I'm 167cm tall F so wouldn't mind some some 700 wheels/tyres on the bike if that's possible at all?
Sorry, that frame will not take larger wheels.
Triathlon/aero bikes have minimal clearance between frame/fork and wheels which do not even allow larger tires in some cases. Additionally, bikes equipped with rim brakes will not take different size wheels because the brakes will not line up with the rims.
The assertion about smaller bikes needing smaller wheels to maintain geometry is true.
An XS size sounds too small for someone 167cm (5'4 1/2"). As you bought it used you may want to consider selling it and looking for a bike the next size up.
Trek dealer here.
The XS sized Speed Concept was designed around someone who is 147cm to 155cm. That size was discontinued in 2016.
Unfortunately, not only is this bike the wrong size for you, but you will be unable to put 700c wheels on it. The frame was manufactured around the 650c wheel-size and simply wont fit 700c wheels in either the rear dropout or the fork.
I highly recommend getting a properly sized TT bike. They are uncomfortable enough as it is!