How can I earn enough promotion points to get promoted to E-5 without schools?

Options for schools might be limited but nothing and no regulation says that you cannot flood your command with requests for schools. It never hurts to submit, submit, submit and to write letters to that same effect.

That said, pursue higher education, excel at physical fitness, at weapons qualifications do the best you can as this adds in as well and when given the chance go before soldier boards. Soldier of the month awards you a set number of points as does soldier of the quarter and year etc. Volunteer in your community as this can get you an award worth points. Your OD badge gets you points, strive to be a senior OD.

Get with your command as they can show you a breakdown of a promotion point worksheet and areas that you can work without needing army specific schools that will add up. You are a ways out from even becoming E-4 (P) yet so you have time.

Not too many E-4 have piles of MilEd, but you do have to get SSD and BLC done. Without those, you are dead in the water. I would encourage you to enroll in CivEd and get your military training on your transcript. This step is often overlooked and can get you a leg up as well as several steps closer to earning a degree.
You are in complete control of your PT score. Get to the gym.
Awards are a little more nuanced, but in order to earn one, you have to be in a position to excel. Volunteer for exercises. Seek out additional duties.
You have time, and I like where your head is. Now get after it.

Focus on college education. Although special skills training is important but not a deal breakers when it comes to promotion. However, college gives you more bang for the buck!

Civ Ed! It's damn near free while you're in need of it when you get out. A quick thing to do is enroll in school and turn in your JST. It'll turn into credits which will turn into points. As a PFC you may not get much but when selected for promotion you'll go to schools and you can turn in your JST again. I can tell you from personal experience that I've turned in my JST about four times in my career and I've received about 45 total college credits which is a little over a year of school....... for free!

You can see some trends. There's what you can control and what you can't.
What you can:
College, PT, weapon qual, correspondence
What you can't:
Awards, mil schools (more can't than can), and the board members opinions

Do what you can for the "can't" stuff and max out your "can" stuff. Above all, be a good soldier. Be a leader before you are put in a leaders position. Plenty of people make E5, and that's what they are...E5s. They become lazy, treat their soldiers like crap, and bring down the force. We need Sgts. 5 types of leadership, know em and apply them. You can lead from a PFC/SPC position. Get to know your PSG and 1SG they have a lot to say within your promotions.

Having started in the 94 CMF, I deeply feel your pain on this. Start hitting those correspondence courses. Enroll in a school as soon as possible to start making use of TA. When you enroll, send over your Joint Service Transcript. Going from Tradoc to WLC with 94F I got all my electives and most of my math/science credited which saved me time and the Army some small bit of money.
As SSG Grierson said, hit them boards. Start performing well, you get awards. Keep performing well, when an incentive school does come down the line you're more likely to get nominated by your leadership.

Have you considered doing extracurricular activities like volunteer work, or getting qualified for other job duties on post out side of your MOS? In the Navy having qualifications in other watch standing positions through our Personal Qualification Standard (PQS) can help you stand out from your peers thus giving you a higher value to you command. Maybe you could even Shadow some of the Higher watch standing stations on your off time. Doing Volunteer work might sound a bit odd but it could help you achieve awards and recognition as your actions bring a positive light to the military. Also I don’t know how the Army handles evaluating your technical knowledge in your MOS but in the Navy we have 200 quest test about 50-75% of it is in Rate (read MOS) knowledge and the remaining is basic military knowledge, like Military history, recognizing other branches rank insignias, grooming standards etc. So reading up on you gears technical manuals could help you gain that in Rate (MOS) knowledge that could not only save your bacon in the field but show that you are dedicated to being a better Soldier who can make the best of his equipment.

Correspondence courses, volunteering (Outstanding Volunteer Medal), college courses.

The fact that you are pinning PFCand already thinking about being an NCO is outstanding. Learn the Creed, study for the board, and do what you can to pick up those points!

You need to max the following events, in this order--> APFT (or ACFT in a year or so) --> Weapons Qual --> Correspondence Courses (ALMS, JKO, etc) --> SSD1 --> BLC (Make Commandants List) --> A quick, 'for-profit' online college like Purdue Global (formally known as Kaplan Online). I only recommend a 'for-profit' online college for speed if you are trying to accumulate points in a quickfast. I would advise a real degree from a more reputable source since you are "about to pin PFC" and you still have a year or so at best before you go to the board or are even ready to become a NCO.

I know how tough certain MOS's are to get promoted in. IT was a while ago with different requirements but out of 1000 possible I had to have 750 points to make E-5 and 966 to make E-6. I did it in 6 years so it can be done if you are willing to do the work!. Go to the education center. see what schools are offering classes - and take what you can. Civilian Education can really help add to your points - get your military education evaluated by the school - that can earn you some extra college credits - depending on the school. Volunteer for extra duties. See if there are boards you can go to, Soldier of the Month, etc. Get that experience under your belt. Work on your PT Score, my worst event was the run.....ugh. It is never to early to start - glad you are thinking ahead for your career.