Are there Pre-K options with no qualification requirements?

My daughter will turn 4 this summer and she wants to go to school. We think it will be good for her to get more social interaction and learn how school works. We don't meet any of the qualifications for Pre-K though. We are in NW Harris County, Champions Forest/Willowbrook area.

Anyone know of any options or have any recommendations? I got something in the mail from School of Science and Technology, but it's a lottery and we're not sure whether we still have to meet any of the usual qualifications. We applied anyways though.