Can Reclass get 11B with Airborne contract?

As stated in previous comments you can always request it. Army is trying to build up it's combat arms branches and giving 10k bonuses for airborne slots, so it should be fairly easy for you to get it. If not proved yourself to your Drills and get a slot in OSUT. That's how I got mine.

You may be able to pick it up in OSUT.

They lied to you, I got an Op 40 as PS. 9B (below) is for PS who are already trained, 9A is for those that got approved to reclass. ex. PS 19D approved to reenlist 11B.

Assuming you pick something the Army actually needs. In your case you want 11B, which they pretty much need all the time.

9–8. Enlistment Program 9B, U.S. Army Station-Unit-Command-Area Enlistment Program
This program is available to qualified NPS, PS, glossary NPS, and ACASP applicants enlisting for the minimum term
of enlistment authorized by REQUEST. Applicants under the age of 18 will not be considered for, nor assigned to
overseas locations.
a. Under this program, enlistee is guaranteed—
(1) For NPS, PS with training, or glossary NPS with training—
(a) A specific MOS or career management field.
(b) A first assignment to a station, unit, command, or area.
(c) Airborne training if REQUEST option four with a committed assignment is selected.
(d) A minimum of 12 months from arrival date at the first duty assignment.
(2) For ACASP, PS, or glossary NPS (which may require prerequisite training)—
(a) A first assignment to a station, unit, command, or area.
(b) Airborne training if REQUEST option four with a committed assignment is selected.
(c) A minimum of 12 months from arrival date at the first duty assignment.
b. All enlistees must meet prerequisites before and after enlistment, per DA Pam 611–21.
c. Primary enlistment options available for enlistment include—
(1) REQUEST Option 4: U.S. Army Airborne with First Assignment.
(2) REQUEST Option 7: U.S. Army Buddy Team.
(3) REQUEST Option 18: U.S. Army First Assignment Only.
(4) REQUEST Option 19: U.S. Army Station of Choice.
(5) REQUEST Option 20: U.S. Army Select Station of Choice.
(6) REQUEST Option 21: U.S. Army Select Unit/Station of Choice 2 Year Stabilization.
(7) REQUEST Option 23: U.S. Army Cohesion Operational Readiness Training (COHORT).
(8) REQUEST Option 24: U.S. Army 2 Year Category IIIB with First Assignment.
(9) REQUEST Option 25: U.S. Army Security Assignment.
(10) REQUEST Option 26: U.S. Army 2 Year NPS.
(11) REQUEST Option 30: U.S. Army 2 Year PS.
(12) REQUEST Option 34: U.S. Army Select Unit.
(13) REQUEST Option 40: U.S. Army Airborne Ranger.
d. Applicants will be informed of the following:

It never hurts to ask. Not going to say it is impossible but you can ask for it in there. You may get it, you may not. You are reclassing to the needs of the army so that is always iffy.

Once you get to your first unit, after you've been there a year or two, you can request airborne through your branch manager. You won't get into an airborne unit without being airborne, and a non airborne unit cannot send you there.

I did this myself so I know the answer has not changed in all the decades. When you transfer from National Guard to Active Duty your considered Prior Service. At the time I enlisted they told me to put my preferences on my preference list since it was a time of demand they would probably look at that. I was not cycled through OSUT again so I could not use that method. So the way you do it is #1 put it on your preference list. I did and I got 101st via my second assignment...though not really an Airborne Unit I got into Airborne Corps. #2 you can get it via enlistment to a specific duty station I believe. #3 which is very, very rare. Some units in Airborne Corps still get Ranger and Airborne school slots handed out. When I was with the 101st it was like 1-2 slots per company a year............that was peacetime and the 1SG and CO used the slots for retention (you had to sign another enlistment with PDA). BTW, your enlistment preference list sticks with you until you change or update it. #1 on my preference list was a unit in Germany (got that). #2 was an airborne unit (got 101st on my second assignment). So they do look at your preference list, when they can OR they did in my case.