Getting the exact crafting material you're looking for can be tough. As with all mechanics that deal with probability, droughts are common. But don't despair! If you utilize all the resources at your disposal, farming doesn't have to be such a chore. Here are some things to keep in mind:
A Strongbox can contain up to 24 different items.
Does that mean if you open 24 strongboxes you're guaranteed to get the item you're looking for? Unfortunately, no. It means that for every strongbox you open, there is a 1 in 24 chance of getting what you're looking for. Your first strongbox? 1 in 24 chance. The next one? 1 in 24 chance. The next one? 1 in 24. And that's assuming you're only opening strongboxes that contain the right materials! So make sure you're not only maximizing how many strongboxes you're opening, but also that you're only hitting fleets that drop the right strongbox for you.
Crafting fleets have a higher drop rate than the usual drop rate of blueprints, but it can still be tough.
These are a great option if you have fleets that can auto these targets, or for when there isn't a Supply Run currently happening.
Supply Run fleets have a 100% Strongbox drop rate!
These Strongboxes are also tailer for a specific ships upgrade tree (IE: A T4 Dread Battleship Box will only contain materials that can be used in it's upgrade tree). Make sure you take advantage of absolutely every Supply Run that you can!
Monthly events offer Core Strongboxes as a prize in exchange for event points.
These Strongboxes offer a much more focused range of cores, and the Elite Strongboxes guarantee at least one T4 Core. Don't see any tech you're interested in? Spend your points on getting those Core Strongboxes for some guaranteed crafting materials.