How can I get ahold of the Infantry branch manager?

They're all working remotely so you'll need to email them. You're only at 24 months on station so it's not time to move you.

HRC/Branch Manager are on telework, you can only reach them by email. If you go to the HRC webpage, and search Branch Manager for your MOS, it’ll give you their contact information. Good luck to you.

From my experience here recently, I can tell you that it is a very hard time to reach branch managers and PDNCO's. A lot of people are being effected by COVID, including their work schedules and they are probably no different. I could not reach my branch manager, so I reached out to another branch manager in the same CMF and they gave me the guidance that I needed. I hope you get the help you are looking for.

I would try emailing them. That seems to work better.

1. What exactly do you need to talk to the branch manager about after just 24 months?
2. Have you updated your ASK preferences online at https://www.ask.army.mil/ask/
3. Have you gone to S1 to update your deployment history and other personal information (Exceptional Family Member Program, Married Army Couples Program, submit appropriate High School Senior Stabilization requests, etc).
4. When you have reached 36 months time on station, communicate with your Infantry Branch Professional Development NCOs / Assignment Managers to review your assignment options and desires.

Enlisted Infantry Branch Manager page
https://www.hrc.army.mil/Enlisted/Enlisted%20Infantry%20Branch%20Leadership

Enlisted Infantry Assignments info
https://www.hrc.army.mil/content/Enlisted%20Infantry%20Assignments

All the assignment manager info is on the HRC site (you'll need your CAC).
Bear in mind two things...
1) COVID has made manning schedules very wonky.
2) Until you gain a bit more rank, branch could care less what your preferences are, unless there's EFMP or similair circumstances. They have hundreds of calls and emails daily for exactly the same reason you're calling. The volume exceeds capacity. So they have to triage, and that's generally by rank and special considerations.

What are you trying to accomplish? I never had a reason to talk to a branch manager until I was a much higher rank BUT details define the answer.

Different terms for different branches. I thought this was a joke your command was pulling on you. Kinda like, find batteries for a chem light. A manager for the grunts???
We call them monitors.

Fort Bliss is one of the last frontier posts still run by the Army and was originally established to protect settlers from Comanche and Apache raids. Later the incompetent Confederacy took the post for about a year before a motley crew from California working on the side of the Union booted them out. Even later still the post became a focal point in defense of Poncho Villa's cross border raids which took place along the border anywhere from approx Fort Bliss all the way to Laredo, TX. So the post has a lot of history but it's in the middle of nowhere and you can thank the 3rd Infantry "Old Guard" for picking the location.

Ah you are at Bliss, you have my complete sympathy, hope you get out of there as soon as possible.