Mr. Neal Katyal, who introduced Gorsuch to the Senate Judiciary Committee during the Supreme Court Justice's confirmation process, represented the town of Chester, New York, which was the petitioner of the case.
Chief Justice John Roberts welcomed Gorsuch to the court before oral arguments began.
Gorsuch responded by thanking Roberts and the other justices for the "warm welcome" that he had received.
"I'm sorry for interrupting, counselor", Gorsuch said.
A more elaborate investiture ceremony will be conducted in the weeks to come.
In May 2006, Gorsuch was nominated by former president George W Bush to take up a position at the US Court of Appeals for the Tenth Circuit.
The court will have its full complement of nine justices, five conservatives and four liberals, for arguments for the first time since the death of long-serving conservative Antonin Scalia in February 2016. The religious liberty case has the potential of becoming the term's most important case. His questions focused on the text of the federal statute at issue. If Gorsuch participates in that one, the cases that could be in front of him include North Carolina's bid to revive its voter-ID law and an appeal by California residents seeking to carry handguns in public. At one point, Gorsuch referred to Katyal as "my friend". But as expected, he remained on the bench.
About 10 minutes into the first case, the new justice opened his mouth and asked his first question, which was both thoughtful and lengthy.
"I apologize for taking up so much time", the black-robed Gorsuch said, sitting back in his high-backed chair and smiling.
President Donald Trump praised Gorsuch in a formal statement released by the White House saying, "As a deep believer in the rule of law, Judge Gorsuch will serve the American people with distinction as he continues to faithfully and vigorously defend our Constitution". SCOTUS Blog explained that the MSPB has claimed that it does not have "the authority to rule on an employee's claim because the employer can not appeal the allegedly wrongful action, but the employee also alleges that she has been the victim of discrimination - a so-called "mixed case'". Lawyers for the church say the state's action violates the Constitution.
If a federal prisoner sued the Bureau of Prisons for not providing meals that are consistent with his religious beliefs and 80 other prisons joined him, Gorsuch asked, would the other prisoners have to show standing in order to get their own meals?
While it is unusual for junior justices to ask so many questions during oral arguments, the court does not have strict rules on questioning.
But the case may fizzle out.
The case involves a debate over the separation of church and state. The church applied for a state grant that helps fund playground restoration with used tires.