The answer is:
After they rested a few days, the aliens revived sufficiently to explore.
Subordinate or dependent clauses, such as "After they rested a few days," do not express a complete thought. They must be joined to at least one independent clause with a relative pronoun or a subordinated conjunction.
In this case, the sentence begins with the dependent clause, which starts with a subordinating conjunction like after. As a result, a comma must separate the dependent clause from the main clause.