Does getting an offer from a U.S. phd program earlier than normal mean getting a relatively better offer?
I'll assume you are talking about a department that admits students via a single admissions committee (rather than offers from individual professors or groups, in which case all bets are off regarding the timing).

As a general rule, getting an offer earlier is a sign that the committee is more interested, but that doesn't mean the actual offer will be better in any concrete sense.  Often there will be a first wave of offers, which may be followed by additional offers depending on how many people seem likely to accept.  Sometimes the further offers are explicitly described as a waiting list, but sometimes the only distinguishing factor is that they come later in time.