A such law would literally reinstate the pre-Christian religion of ancient times (from over 1,000 years ago or even earlier).
The First Amendment begins with the Establishment Clause:
Congress shall make no law respecting an establishment of religion ...
The Supreme Court has been clear that this prohibits an "official denominational preference" (Larson v. Valente, 456 U.S. 228, 245 (1982)).
The Establishment Clause also applies against the states via the Due Process Clause of the Fourteenth Amendment. See Everson v. Board of Education, 330 U.S. 1, 15 (1947):
The broad meaning given the Amendment by these earlier cases has been accepted by this Court in its decisions concerning an individual's religious freedom rendered since the Fourteenth Amendment was interpreted to make the prohibitions of the First applicable to state action abridging religious freedom. There is every reason to give the same application and broad interpretation to the "establishment of religion" clause.
Neither a state nor the Federal Government can set up a church. Neither can pass laws which aid one religion, aid all religions, or prefer one religion over another.
Governments can pass whatever laws they choose.
A dictator can dictate laws, and forcing a religion on people would in a historical sense be fairly normal. "Pagan" gods frankly have no more or less standing under law than a more modern Jehovah or Allah. Dictators enforce their decrees via threat of fines, imprisonment, or death.
People can similarly democratically create whatever laws they choose. US voters could force amending the Constitution and create laws requiring the daily attendance at worship of whatever god they chose, again, enforced by threat of fines, imprisonment, or death. Smaller groups of like-minded religious people often enforce their beliefs on their congregation through social pressure as well, such as the threat of excommunication and subsequent shunning by the community.
The presence of present-day theocracies would seem to indicate that it isn't particularly difficult to establish a government with religious requirements.