Hey, I’ve been there, we all have. Ascension materials are one of the most scarce items in this game (along with solid 4* and 5* heroes for some), so at least you’re a little ahead of the curve on your heroes.
I was short on compasses when I first started; I don’t think I started seeing them consistently come in until about three to four months in. When you can complete intermediate (and advanced) in challenge events, and complete all rare quests, you’ll be on a steady path of getting the mats you need to ascend.
If you do more pulls than purchasing mats, you will have a shortage of mats a lot sooner than if you never purchased anything at all. If you go this route, you’ll be given a choice on who to ascend, rather than just ascending whoever you have at that time. So there is an advantage to summoning heroes with cash, but only a slight one.
Are you in an alliance? Are you participating in wars and hitting the Titan? What star titan are you hitting? How many chests do you fill a day? Are you watching Mystic Vision every chance you get? Are you finishing every rare quest and challenge event? All of these are important questions, and the biggest ways to receive mats in this game. I’ll explain below:
All In-Game Opportunities to Get Unfarmable Mats:
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Rare Quests - These always include a guaranteed 3* and 4* material. Best consistent resource of mats in this game.
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Challenge Events - These happen monthly, guaranteeing you 3* mats upon completion of intermediate and advanced
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Seasonal Events - These happen annually (and right now, there are four seasonal events in rotation), including at least one guaranteed 3* and 4* mat (sometimes two)
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Titan Loot - Loot Tier IX is the most ideal for loot (three mat rolls), giving you three slots to potentially get unfarmable mats. A+ on a 6*, A on a 7*, B on an 8*, and C on a 9* Titan. Anything below that would be two rolls
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Wanted Mission Chests - Very rarely do these have mats, but I’d say at least weekly you’ll see at least something of note, especially if you skip the wait time to fill several in one day. Definitely a solid way to spend gems when you’re chasing after mats and elementals
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Elemental Chests - Filling more Wanted Chests a day will give your more opportunities for an elemental chest to pop up in it’s place. These always have two slots for mat rolls (3* or 4*). Although, they can be farmables 3* mats, these chests have a lot of other goodies inside as well
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Mystic Vision - If planned correctly, you can watch MV ~1.5 times a day. These drop mats even more rarely than chests, but it does happen.
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War Loot - Okay, I very rarely see anything good from war, but it’s possible. Always worth participating anyway, because you never know if you’ll get something good from it.
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War Chest - These are similar to elementals, where they include two slots for mats (3* & 4*), but they could also be farmables 3* mats as well. The only thing is, you’ll want to be sure you’re participating in every war to ensure your chest is at 100% participation, in order to get the two mat rolls. Anything less than 80% (I believe) doesn’t amount to nearly as much.
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Atlantis Portal - After you make 10 pulls in the Atlantis portal, you get a chest with a guaranteed unfarmable ascension item. You’re only allowed 9 chests per portal, but it’s a great way to get the heroes you’re after, while also getting a few mats you may need. If you don’t fill all 9 chests that round, your progress will carry over to the next portal (ex. Only did 3 pulls, chest next time will read 3/10)
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Purchases - Occasionally SG will offer pop-up deals, ranging in price, with guaranteed mats. They’re usually good deals, with similar gem costs to the shop, but also include mats and other goodies. If you already plan to make pulls at a later time, these offers are better than buying gems straight from the shop. Honestly, if you’re on a budget, I would never buy gems from the shop and only purchase these deals since they’re more cost- effective in the long run.
Honestly, the best tips I can give you to fulfilling most of these would be to start working on your 4* teams. 4* can be used in intermediate and advanced [in the challenge events] and they’re also strong enough (once maxed) to complete everything listed above. They’re your best bet with helping you get more mats for more of your heroes. 3/60 4* can complete intermediate, and I believe rare quests as well, although you may have to use quite a bit of items, or the 75 gems to continue; it’s definitely worth it if there’s an unfarmable mat involved.
Unfortunately, this game is all about patience. Once your team becomes more developed, and you yourself become stronger, you will see an increase in mat drops. It may take a couple of more months until you get there, but after awhile, you’ll eventually start swimming in 3* mats and start really lacking 4* mats. This game is definitely a grind, but that’s the beauty of it. You will always have to work for whatever you have; money doesn’t change that. It can be frustrating at times, but it’s also what makes this game so great.
While you wait, take all of your important 4* to the mat wall, and if you run out of 4* to work on, start on some 3*. They can be used in the beginner tier, which includes a free flask upon completion. Plus, they’ll help fill out your roster for stacking and war, and are very cheap and quick to level.
If you ever have questions, this forum is a great resource to learn everything regarding this game. & This community is awesome, so if you have any specific questions that you can’t find the answer to through a search, there are plenty of people here that would be happy to help (including me).
Good luck on your mat hunt; I hope you get all of the necessary mats that you need soon. 
