At the risk of sounding philosophical which came first the timelord or TARDIS? In the show it is stated that TARDISes grew, it was also stated that it takes thousands of years to grow. Is there canon evidence on which evolved first?
There is no canonical answer to the question. Frankly, the Doctor has given so many different answers for how his TARDIS came not only to exist but to be in his possession that nothing we have heard on screen can actually be accepted as gospel truth on the subject. The Doctor is an unreliable narrator!
- Susan (his granddaughter) claims to have invented the word TARDIS herself, but not only do other Time Lords use it routinely (once we start to see them), they even pun on it. The War Chief provided the War Lords' race with "SIDRATs" -- simple, remote-controlled TARDISes.
- The Doctor claims on some occasions to have invented the TARDIS himself! (Tomb of the Cybermen).
- The Doctor starts out hinting that he and Susan are exiles of some political bent who cannot go home. Later, he just says he stole the TARDIS because he was bored. Later, we learn the TARDIS stole him (but he was guided to her by Clara!).
- Until the modern series, the TARDIS was clearly a technological, not a biological, contrivance, although it was glossed very early on to have a kind of intelligence, albeit one that found communication with mere people very difficult and wound up doing it indirectly. Only in the modern series is it suggested that TARDISes are grown, but the Doctor's is still generally seen as being repaired and tinkered with like a machine, and indeed, more recent sets have downplayed the organic-TARDIS idea.
Long story short, The Doctor lies; the writers' don't all agree with each other; and we really just don't have any clear idea where any of the Time Lords' technology came from. We know Omega had a hand in creating the initial power source (a supernova) and it's implied that Rassilon built on that research to capture the Eye of Harmony (the nucleus of a black hole) and really, that's about it.