For Hurjet we can take India's Tejas Naval for comparison, they are well-matched in size, weight and engine size - ofcourse the Naval version of Tejas has greater wingspan which is around 60% greater than Hurjet.
I believe navalising Hurjet would be the quickest way- but if a naval version is being developed parallel to training and light attack versions of Hurjet - we may see it within the decade or sooner.
Yes the important thing is that Turkey develops the robust ecosystem around hurjet.
Turkey has good industrial capacity to do this quite quickly....a transition to naval design on same platform can be achieved quite quickly.
Once India hit the ecosystem development intensity needed, it was not hard to get variants quite quickly...this is why the schedules for Tejas Mk2/TEDBF are lot more aggressive lately (just couple years away or so).
Our Air Chief in aero-india gave interview that the scope of orders for these variants will depend on the AMCA schedule and what development and production capacity will be tied up there if that timeline comes at quicker potential. If it will take time, then theres more need for interim variants of mk 2 Tejas etc basically.