It has been a fantasy for many who have passed through the gates of Yankee Stadium’s hallowed Monument Park: Imagine if these greats could have played on the same teams at the same time? How would you begin to construct a lineup card with the likes of Babe Ruth, Joe DiMaggio, Mickey Mantle and Derek Jeter at your disposal?

Major League Baseball, in conjunction with Out of the Park Baseball, is giving us the opportunity to get that incredible squad on the field. The MLB Dream Bracket presented by DraftKings began on Monday, a 32-team best-of-seven simulation featuring all-time teams for each of the 30 current Major League franchises, as well as teams consisting of Negro Leagues Stars and 25 & Under Stars.

• Full bracket and schedule | Dream Bracket rosters | Play FREE: DraftKings Dream Bracket pools

The 26-man rosters for each of the teams, compiled by MLB.com’s beat reporters, consist of 15 hitters and 11 pitchers. For the simulation, players are rated using the average of their three best seasons on a single team. Rosters were constructed with balanced depth to specifically compete in a simulated regulation game.

And after dispatching an all-time Mariners club in a six-game series -- once again getting revenge for the 1995 American League Division Series, as they did in the 2000 and ’01 postseasons -- the 27-time World Series champions are headed to the next round. The Bombers will face the Indians, who outlasted the Negro League All-Stars in the first round.

• Box scores

Here is a recap of how the Bombers’ set against Seattle played out:

Game 1: Yankees 3, Mariners 2
Seattle struck first, as Jay Buhner belted a two-run, second-inning homer off Whitey Ford. Matched against Randy Johnson, New York trimmed the deficit on Reggie Jackson’s third-inning RBI single and the Yanks claimed the lead in the sixth as Tony Lazzeri doubled home Alex Rodriguez, advanced on a Jeter single, then scored on a Big Unit wild pitch. Lefty Gomez picked up the win with 2 1/3 innings of scoreless relief, and Mariano Rivera recorded the final three outs for a save.

Game 2: Yankees 1, Mariners 0
Right-handers Red Ruffing and Félix Hernández locked in a fantastic pitchers’ duel at Yankee Stadium, decided by Lou Gehrig’s seventh-inning, opposite-field home run to the left-field bleachers. The Iron Horse’s blast was all the support Ruffing would need, as he limited Seattle to two hits over 7 1/3 innings. Rivera recorded four outs in relief and Goose Gossage entered (hopefully in the pinstriped bullpen car) to seal the victory, striking out pinch-hitter Alvin Davis looking.

Game 3: Mariners 4, Yankees 0
The series shifted to T-Mobile Park, where the Mariners supported Jamie Moyer with three fourth-inning runs off Ron Guidry. Bret Boone knocked an RBI double before Nelson Cruz launched a two-run homer to the right-field seats off “Louisiana Lightning,” who also permitted a solo Boone homer in the sixth. Moyer limited the Yanks to three hits over seven scoreless innings, striking out six without a walk.

Game 4: Mariners 3, Yankees 2
The series was evened in heartbreaking fashion for the Yankees, who were handcuffed by Mark Langston for eight dominant innings before taking a ninth-inning lead on RBI doubles by Jackson and A-Rod off Kazuhiro Sasaki. But Seattle did not roll over. John Olerud touched Rivera for a one-out single, and the Yanks summoned Dave Righetti, who issued a walk to Buhner before Ichiro Suzuki legged out a run-scoring infield single. Sparky Lyle issued a game-tying walk to A-Rod (the younger Seattle version) and lost Edgar Martinez on a 3-2 pitch, forcing home the winning run.

Game 5: Yankees 9, Mariners 4
New York recovered in Game 5, never trailing as they reclaimed a series lead. Mantle hit a three-run, first-inning homer and Yogi Berra slammed a solo second-inning blast, both off the Big Unit. Seattle pushed back in the fourth on back-to-back Boone and Cruz homers off Ford, but Jackson responded with a three-run blast off Johnson in the sixth. Buhner knocked a run-scoring hit off Ford in the home half of that frame, but DiMaggio laced a two-run single in the ninth off Freddy Garcia. Waite Hoyt hurled 3 1/3 scoreless, hitless innings to pick up a save.

Game 6: Yankees 2, Mariners 1
The Yanks advanced to the round of 16, with Ruffing firing 7 1/3 strong innings of one-run ball to clinch the series in the Bronx. Ruffing settled in after Ken Griffey Jr.’s first-inning sacrifice fly, walking one and striking out seven. New York broke through against King Félix in the fourth inning as Berra slugged a two-run shot into Monument Park. Gossage recorded the final two outs of the eighth inning and Rivera struck out one in a perfect ninth as the Yankees celebrated. Ruffing finished the series 2-0 with an 0.61 ERA, while Berra was 7-for-21 (.333) with two homers.