In my experience, if the objection is due to the typical dislike of change, then simply being persistent and leading by example will win the day. Make it clear that she cannot go out if she does not have a mask, and be gentle but firm, reminding her why it's important - "This mask will protect you from getting sick, and will protect everyone around you from getting sick if you do get sick."
Do be conscious though that it's possible her objection is more specific. Similar to my son's objection to denim, which is likely due to sensory issues, it's very possible that she objects not because of obstinance or dislike of change, but because it is uncomfortable for her. As such, try to work out ways to make it less uncomfortable. There are different kinds of masks, some of which attach in different ways; for example, for our children we have masks that don't have elastic, but simply are longer pieces of slightly stretchy fabric that have holes cut in the fabric for the ears. Those seem to be somewhat more comfortable; the elastic strands behind the mask are uncomfortable for many.
Also consider the shape - she may prefer a rounder mask with more substance to it, for example, that stays away from the mouth and nostril, as opposed to a flat fabric mask that is closer fitting. Both protect effectively (given they are constructed properly), but it may simply require some testing to find what is comfortable for her. Work with her, make it clear you're trying different things, and ask her to try each thing once. Remind her what benefit she's getting - i.e., getting to go play at the park or whatever - and hopefully she will cooperate, at least for a short period of time.
Finally, definitely focus on that last bit: short. Children shouldn't be expected to wear masks for hours at a time. Fifteen minutes is about the most I'd expect at that age. You mention this in your question, so good job thinking of that - but also remind her it will be a short time, as she may not realize that internally (time is hard to comprehend at 3!)