Winning is a thing that is supposed to happen during an event.
Before the event, of course, there are many competitors eager to win.
I need a nice word or phrase to express eagerness to win — but not winning itself.
Ambitious describes an eagerness to succeed and also implies that success has not yet been attained.
Alternatives that are quite similar to eagerness to win are
Maybe these works in your context, too
I think eagerness to win is a good alternative. I can´t really think of a better term that expresses exactly that, but Enthusiasm may be close, though. The problem is that with no additional context, the enthusiasm could be taken for other aspects of the competition, and not specifically for winning.
You could consider: pumped up, fired up, psyched (anybody else remember the cheerleaders shouting "P-S-Y-C-H-E-D psyched is what we want to be!")
Motivation - one could write of highly motivated competitors
A couple more:
'Desire for victory' implies the person, group or team have set their sights on winning and will only be satisfied if they emerge from the scenario as victorious.
'Lust for victory' implies that the person/people are as equally determined, and may even resort to slightly unsportsmanlike behaviour in order to win (rigging a competition, cheating during gameplay or engaging in subterfuge)
There is a perfectly adequate word which means "eager to win". And that's "competitive".
And that's shows the redundancy in what you're trying to say, because it leaves you with:
Before the event, of course, there are many competitive competitors
Pretty much by definition, if they're competitors, they're expected to be competitive.
If you want to say that some entrants are more competitive than others (and imply that some entrants aren't serious competitors at all - maybe they're just there to make up the numbers), then say that.
Or are you trying to take it down the route of saying that although there are many competitors initially, many get eliminated despite their best efforts?
All in all, the question probably needs a little more context to make sense of it.
Two words come close to me, at least in usage.
One is thrust, as in "We were stymied in our thrust for victory."
The second is the commoner hunger: "The team had an insatiable hunger for victory."
Taken in context the word determined might fit:
Before the event there were many determined competitors.