Before getting a good answer to your question, you need to provide some more specific info.
Firstly, what would you consider "competence"? This is VERY subjective and you have to define this right at the outset. I think the best way of defining your conception of competence to us, since in Wrestling we do not have any type of belt system or the like which you see in BJJ or Judo, is to say what level of wrestler you would like to "hang" with (by hanging I mean being able to take them down and turn them just about as often as they are able to do to you).
Secondly, what kind of a grappling background are you coming from and what level of proficiency have you reached in that art?
Lastly, what kind of game do you have in that art? How strong/weak are you at your takedowns (since takedowns figure VERY prominently in Freestyle Wrestling since you will spend the majority of your time on your feet)? How strong of a "base" do you have on the ground, i.e. are you difficult to sweep, if you are coming from a BJJ background, or are you difficult to sweep or trun, if you are coming from a Judo background?
Despite not having the answers to the above questions, I'll still attempt to answer your question based on my experience as a wrestler first and foremost, and then based on my experience with BJJist/Submission Grapplers and, recently, Judokas.
If you at least have good (for BJJ or Submission Wrestling's Standards) takedown defense, if you are coming from a BJJ or Submission Grappling background, and are not a guard puller/flopper and have some knowledge of takedowns, and you like playing either like playing a top game more than willingly going to the guard, training 3 times a week at a quality club with quality training partners and while getting in at least a couple dozen matches at competitions, I'd say it would take you 4 years to get to the level where you can "hang" in a freestyle wrestling match with a guy who started at a Div. I school at least 2 years in college and who had a winning record both those years.
If you are coming from a Judo background, I'd shave the number of years down to 3 just because Judokas seem not to be guard floppers, are looking for the pin on the ground, and are already used to maintaing a base that an opponent cannot attack, something very important in Freestyle Wrestling, and have, in my experience, MUCH better ability to avoid being swept than their BJJ counterparts who have a similar amount of training. The only "problem" would be adjust to the fact that there is no-gi and learning how to make a fairly upright stance work for them in wrestling (which can be done).
An important note though when it comes to the difference of learning or becoming proficient at wrestling when compared to BJJ or Judo is that it is almost absolutely essential to get in some good competition experience because it will speed up the learning curve by LEAPS and BOUNDS. I've seen some Judokas and BJJ'ers who have never competed and to me that is inconceivable when learning how to wrestle. No matter how hard you go at it in the practice room, there is something WAY different about applying what you know in the practice room against an opponent who is there to beat you. In the practice room, your partner i s there to make you better and himself, on the competition mat he is just out there to win.
Lastly, in freestyle wrestling, the worse place to be is on your back or in a position where your back faces the mat at all. Exposing your opponent's back to the mat for even a second scores points in freestyle. Make sure he doesn't do that to you.
Hope this helped. If you have further questions or could supply more specific answers to the questions I asked at the top, please do so and I'll be able to give you a better answer.