Can we train at a park?

Yes, and plenty of people prefer it. Grass is the best surface you will get for free.

Sort out permission first. Every city here writes its own park rules and some want a permit for anything that looks like instruction. Check before you plan on a public space. If it turns into a hassle, a garage is simpler and I will come there.

Look for flat grass, no sprinkler heads, shade at midday, parking close enough that mats are a short carry. The city pages list spots people actually use. Family can come along, which is half the appeal: see who else can be around, plus mats and flooring and what happens if it rains.