The Open Qualifier is a special tournament inasmuch that all players regardless of skills, equipment and tiers play from the back tees. I'm sorry to say, but with the Starter equipment you have no chance to contend.
Oops - you're talking of the back 9 CTTH challenge - different story.
Alas, there, too, you are facing some trouble with your Starter equipment:
- the clubs act on rather low trajectory, making shots "to the spot" virtually impossible.
- their shot length is low, too. Thus you need high clubs to get where you want to => lower trajectory, long roll.
- they, clubs and balls, provide very little spin => adds to the long roll.
I haven't tried the challenge with this equipment, but I'd guess that you have "won" when hitting all nine greens. Honestly.
Your question has a two-way answer.
To become an Amateur, you don't need new equipment. Just play ranked strokeplay rounds, regular and tournaments (except for the qualifier, see above), and you'll be there in no time. You may happily continue without a change until the Tour Pro tier, experiencing longer tracks or faster greens on every change.
To get good equipment, you need credits and certain levels.
Credits: There's a "get free credits" section above, expect small payment and some disencouragement there. I prefer to invest some real cash for my leisure.
Levels: You get XPs from playing, best opportunity is to play one, three or more holes per day for up to 880 XPs for completing a "round". 2nd best and adding to the former is tournament rounds, up to 400 per.
Equipment: You will have noticed that those marketing experts of WGT want to talk you into new&better equipment every day.
IMNSO, low level buys tend to become pointless too soon. Whatever you want to buy, look out for the possible better equipment available at a higher level. In general, unless the need for a change is irresistible,
- do not start to buy wedges before level 18,
- do not start to buy a putter before level 30,
- do not start to buy woods and irons before level 47/48,
- start buying balls as a Tour Pro, work your way through the list from cheap to expensive. Try to avoid using a ball with higher level than your main clubs.
For you, two short wedges may be a good buy. Wait with everything else.