DNA would indeed -- at least from our perspective -- seem a quite likely candidate for carrying genetic info.
If life develops more frequently than usual on Earth-class planets around Sun-class stars (and the only data point we have suggests it does)...
...then, assuming it develops on earliest feasible opportunity... one could indeed construct a model of probability (admittedly with vast gaps, but not intentional ones) drawing from similar environmental starting conditions to suggest the common occurrence of DNA.
Then again, I try to never underestimate the power of countless random experiments in a humongous range of conditions... of yielding different pathways to achieving the same functionality.
Also, life has properties which favour having a distinct face. The first strain of life starting... will most probably cover a planet before another can start. Following experiments may succeed, but are likely to get snapped up by already developed life -- which is unlikely to undergo radical changes in its genetic mechanism, unless the initial invention really was sucky.
I think so because changing the encoding system might render useless an existing and useful codebase -- which has some value to counterbalance the benefit of a more efficient encoding system. Somewhat differently from software engineering, form and function are closer linked in biology. Change of format generally means loss of function.
At some points, benefit from change would naturally overcome the cost of conservation -- and encoding systems would change. However, this seems likely either early in development (little existing codebase) or much later, when technically advanced sentients make their own abstraction layers independent of genes.
Also, should life also easily appear on different classes of planets, around stars of different kind and generation... it would be far less likely that DNA would be widespread.
The earliest hope of finding out... is two days from now.
Unfortunately the hope of finding something on Mars is relatively small. After that, one can dig up Europa, Ganymede, Io... and whatever nearby place seems lucky.
Finally, one can build a big-ass telescope and observe extrasolar planets. Should that fail, one can repeat SETI with really mean super-receivers and vast computing power in future. Hoping to hear someone talking.
And finally, if nothing adverse happens before, curiosity will no doubt drive someone to get their possibly-encountersuited-butts out of the Solar system.