SEATTLE — Shortstop Amed Rosario, whose talent has made him the crown jewel of the Mets’ farm system, will make his major-league debut on Tuesday night against the Rockies. First baseman Dominic Smith, the Mets’ second-best prospect, is expected to be called up in the next few weeks.

“It’s important for guys like Rosario and Smith to get more than just playing time in September,” general manager Sandy Alderson said. “To make it really more meaningful, it needs to be a little bit longer than that against more regular-season competition as opposed to expanded rosters.”

Despite Rosario’s torrid production with Triple-A Las Vegas (.328 average, seven homers, 58 RBIs), the Mets have hesitated to promote the 21-year-old, citing a crowded veteran infield that would make playing time difficult to manage.

Alderson said the team has long targeted the period after the non-waiver trade deadline for Rosario’s long-anticipated promotion. “It was a combination of just getting through the hullabaloo of the trade deadline and then at the same time allowing some of our other players to get more familiar with some of the other positions,” Alderson said. “Plus, he’s continued to play really well.”

Jose Reyes and Asdrubal Cabrera have shown the ability to play elsewhere in the infield, opening up room for Rosario to play shortstop, where he would be an instant defensive upgrade. Neil Walker has begun working out at first and third, which would open up more opportunities at second base for Reyes or Cabrera.

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Extra bases

Noah Syndergaard (lat) and Matt Harvey (shoulder) have taken steps forward in their throwing programs, though neither has progressed to throwing off the mound. Jeurys Familia (blood clot) also has made progress. “There have not been any setbacks,” Alderson said . . . Robert Gsellman (hamstring) is expected to continue his rehab assignment in the next few days . . . Alderson cited recent ineffectiveness against lefties as the reason Josh Edgin was designated for assignment on Sunday. Said Alderson: “We just felt this was the right choice of the three or four candidates that we had.”