As an older enlistee, what should I expect for a normal Army career progression for a 12B? What else can I do to look better among my peers?

You're not behind your peers, you're way ahead. Your timeline isn't measured in age, it's active duty. You're an E4 with 4 months time in service, and a level of maturity and experience that is a decade ahead of your peers. If it takes you 5 years to make SGT in a combat arms MOS, you're doing it wrong.

Your branch has your Career Map for MOS in Army Career Tracker. This is the gold standard for what you need to work on at what stage in your career to stand out above your peers.

If you push hard enough, you could be a SSG by the time you are 37.

I recommend you pushing hard on the requests for Sapper School. Also, find out what additional duties in your unit are still unfilled (that you can do based on rank) and ask to take charge of those additional duties. Maximize all time available to get civilian education completed. Those hours are worth points. Same with military correspondence education. As soon as you pin SGT, I would recommend you wait one year before submitting a packet for Drill Sergeant. This way, it will give you time under your belt as an NCO before you take that DS route. But, that is just my opinion. Also, find a Senior NCO and ask them to be your Mentor IOT help guide you to your goals as soon as humanly possible.

Drill Sergeant did wonders for my career. Perhaps something to look at when you make E-5, if they still take E-5s.