I am afraid your chances aren't good.
Wheat bread with yeast, gluten-free bread, and wheat quickbread are made in different ways. The wheat bread with yeast is ideally made with several cycles of kneading and rising. A gf bread is not kneaded, just mixed, and then has to rise once. The quickbread is also not kneaded, but it has to be baked immediately, without a rising time. So, if you want to make any of these with a bread machine, you have to use a program that was engineered to deliver the needed conditions.
If your machine has no gluten-free program, then it is unlikely that any of the other cycles matches the conditions needed for gluten-free bread. There is some likelihood that some of the programs that you have can match some kind of recipe such that the result is not inedibly terrible, but discovering such a combination would require a lot of experimentation, and the result will only be valid for your exact breadmaker model. Also, the result is unlikely to be especially good.
In the end, if you are making the bread frequently, it may be worth investing in a new breadmaker, after researching which one has a decent gf-program (and then you will have to find out which recipes work - which may or may not use the exact flour mixture you have). If this is a one-off occasion, just buy the bread from a store. GF-bread is very finicky, and probably not worth the learning curve if you won't make it regularly.