Define "make it big".
To become a truly professional rider, you will need to ride multitudes of horses of different ages and experiences, sit on the lunatics to the schoolmasters, the lazy fat ones to the racehorses. Get you backside on as many horses as you can. ONCE you have become a competent rider on your own and with lessons.
You can have the dream to make it big, but it's not a case of just asking a trainer to teach you have to be fantastic on a pony. You need to get the hours under your belt and the experience to go with it. You sound very young, I'd say you've got plenty more years of experience to go, you're not going to fall off your perch any time soon so no rush.
However money is a requirement unfortunately, as much as you don't want to hear it. In Australia, we have done super well internationally with eventing with most of the team made up of ottb's that the riders have picked up for doggers money. Yes, the horse buying bit can be cheap, but to have the ability to turn that cheap, 'dog' into a star is a whole new kettle of fish. It's not a case of the black stallion, kid has dream and kid tames who who wins everything. It doesn't happen like that. The elite riders have generally worked their backsides off, ridden so many different horses, hooned around paddocks bareback on bucking ponies and ridden some real lunatics. The eventers have more of a chance of 'making it big' than the dressage and show jumpers do, dressage in particular is a very elitist sport when you hit the higher levels. And even now leaking into the young rider classes are super expensive, imported horses that have been trained piaffe in hand in Germany. You can't expect to 'make it big' against people in these disciplines who have mega bucks, no matter hpw good you are, unless you hit it REALLy lucky and get a place as a rider for an elite stable/stud. And even to do that, you need a proven track record as a performance rider, which requires money if you want to be out there beating everyone.
Yep there's the exceptions. We've got a local girl on her ottb/ex eventer who is now competing PSG/inter 1 with great success, but not when pitted against the absolute top of the imports.
Money is a HUGE advantage in the competitive/professional horse world unfortunately.