There is no "equal access clause" in the federal Constitution but there is an equal protection clause. The federal courts have held that equal protection means that the government must generally treat similarly situated persons/groups the same and that the government must have a rational basis for making distinctions between most persons/groups, though a higher standard is applied if the distinction made is based on race, sex, religion, or sexual orientation. Furthermore, the First Amendment to the Constitution requires, among other things, that the government not give preference to one religion over another and that the government not interfere with a person's religious practices unless there is a compelling government interest at stake.
A public school does not have to allow religious activities on its grounds. The First Amendment does not require that the government provide space or facilities for religious activity. But if the school allows persons of one religion to conduct religious activities on its grounds it must afford that same right to persons of other religions who wish to conduct religious activity there.
So the details of your school's policies on this, including why the school will not allow you to meet during school hours, matters. Does the school have a written policy on this? If so, what does that policy say? It also matters what the details are of the groups that are allowed to meet during school hours. What kind of groups are they? If they are religious groups that may be a difficult problem for the school to say you can't do the same thing. If they aren't religious groups then the school is likely on firmer ground to deny your group time to meet during school hours. You also mentioned the possibility that the groups meeting during school hours are faculty led rather than student led groups. That too would be important as that would give the school a rational basis for making the decision it did. Other differences between your group and the other groups may be significant, too.

