You can reach the Master Tier with just the starter clubs and some persistence; I know this because I've done it myself. However, it's in your best interest to get off the Weak WGT Mashies as soon as you can and upgrade to some Real Branded Mashies!
Say what you want about 'drive for show putt for dough', but I believe that with all the long par 4's in this game, combined with the pathetically weak starter clubs (they can't even mash potatoes!), I believe that buying big hitting irons and a driver is the top priority to being able to play when you reach the upper tiers. Hence why I bought a lvl 59 G20 club set first.