The National Football League’s off-season training program normally comes and goes without the fanfare that surrounds the beginning of training camp in July. For the New York Jets and Giants, though, offseason training activities over the next month offer the first glimpses of the substantial additions by both teams.

When rookie mini-camp begins in two weeks, the Giants will greet the six players acquired from this year’s draft. The Giants’ picks were a LSU wide receiver, Malik Nabers, in the first round; a Minnesota safety, Tyler Nubin, in the second; a Kentucky cornerback, Andru Phillips, in the third; a Penn State tight end, Theo Johnson, in the fourth; a Purdue running back, Tyrone Tracy Jr., in the fifth; and a UCLA middle linebacker, Darius Muasau, in the sixth round.

Notably, the general manager, Joe Schoen, did not draft a quarterback and didn’t make a draft day trade for the first time in his three years with the Giants. By contrast, the general manager of the Jets, Joe Douglas, made six in-draft trades this year.

There’s no crystal ball to predict how productive any of the draft picks will be, but Mr. Schoen and the head coach, Brian Daboll, offered a positive assessment of a roster also fortified with the acquisition of 14 veteran free agents, including a two-time Pro Bowl pass rusher, Brian Burns.

“I like some of the moves that we made in the offseason,” Mr. Schoen told reporters following the draft. “We still have work to do, and I just think it’s year three, and we are just going to continue to build the roster and the team.”

The decision not to draft a quarterback looms large and could define this draft.  The Giants, coming off a disappointing 6-11 season, took Mr. Nabers with the sixth overall pick when quarterbacks Michael Penix Jr. of Washington and J.J. McCarthy of Michigan were still available. Mr. Penix went to the Atlanta Falcons at no. 8, while Mr. McCarthy was picked up by the Minnesota Vikings at no. 10. If either player becomes a franchise leader within three years, the Giants will be second-guessed for not drafting either of the prospects.

Barring something unforeseen, the Giants enter the 2024 season with Daniel Jones as the starting quarterback and with newly signed Drew Lock as the backup. Tommy Devito, who led the Giants to three consecutive wins last season, is the third quarterback. It figures to be Mr. Jones’s last chance to prove he is a long-term answer. After signing a $160 million contract last year, he played just six games before suffering a season-ending knee injury. There are three more years left on his deal, but it would be difficult for Mr. Jones to remain the starter if he has another unproductive year.

At least he has a new weapon in Mr. Nabers, who set LSU records for career receptions, 189, and yards, 3,003. Mr. Johnson could play a more pivotal role should Darren Waller decide to retire, as is speculated.

“I’m excited to get the rookies in here,” Mr. Schoen said, “assimilate them into our culture, get on the grass, practice, and then as we observe and evaluate the players as we’re going through it.”

The Giants elected not to sign running back Saquon Barkley to a long-term deal and added Devin Singletary to the new-look offense. “Once we get on the field and see how the pieces work together, we’ll have a better feel,” Mr. Schoen said, adding, “There are some new pieces. What do they do best and how can we accentuate that?”

The Jets off-season workouts officially open Aaron Rodgers 2.0. The veteran quarterback played four snaps before tearing his Achilles tendon in the first offensive drive of 2023. After using free agency to fortify the offensive line and bring in one of the league’s best receivers, Mike Williams, the Jets used their first five draft selections on offense.

They’ll welcome seven draft picks to their rookie camp, claiming a Penn State offensive tackle, Olumuyiwa Fashanu, in the first round; a Western Kentucky wide receiver, Malachi Corley, in the third; and a Wisconsin running back, Braelon Allen, in the fourth round. The Jets had three picks in the fifth round, selecting a Florida State quarterback, Jordan Travis, a South Dakota State running back, Isaiah Davis, and a cornerback from the Canadian Football League, Qwan’tez Stiggers. An Alabama safety, Jaylen King, was added in the seventh round with the final pick of the draft.

The Jets offense should be much improved not only with the return of Mr. Rodgers but also the free agent additions of Mr. Williams, two veteran tackles, Tyron Smith and Morgan Moses, and guard John Simpson.

“We added a lot of quality players to this team,” Mr. Douglas said of the draft. “Our types of guys, guys we’re excited to add.”

The Jets’ first six selections were acquired through trades.  “It’s a good group all the way across the board,” the head coach, Robert Saleh, said. “A lot of great competition, a lot of great character, a lot of guys coming into work who are intrinsically motivated. We’ll throw it out there and see how the cards shake out.”

The Jets and Giants Organized Team Activities workouts continue through May and early June. The mandatory minicamp for both teams is June 11-13.  Meanwhile, the 2024 NFL schedule is expected to be released during the second week of May.

Correction: Braelon Allen was a Wisconsin running back. An earlier edition misidentified him.