Reputation. outdated equipment. officers.

i know its moot but try to keep your reputation up. do this by completing missions and winning battles. sometimes its better to ignore the missions and do your own thing just realize you will take the reputation hit. i spend reputation on research and prevent it from going below 100.

make sure all of your officers are being used. if you have some still in your pool, use them either by creating regiments or give them assignments. you should then receive the ability to recruit more officers as a mission in your HQ. do this a lot and you should get plenty of officers to lead your regiments. make sure your army infrastructure is expanding as you create regiments.

i heard that building colleges eventually yields officers. from time to time i have seen some officers pop up that i did not recruit via a mission so this must be true. build these early

to avoid high expenses, keep your regiments small in places that don't require too much manpower. one location may indicate that it requires only 90 men in a garrison or something to prevent a revolt in the region. so make the regiment size only a company strong. militia are 150 men per company. give these goons your outdated weapons and give your fuller regiments the good weapons.

sell equipment you are not using and and purchase what you can from the market. Trade with Spain and France for weapons. you can trade with the Indians for horses if they have them too. don't forget to make your own muskets as needed.

you can gather quite a few brown bess muskets from winning battles against the british.

Try Hetman's UGAR vids on youtube

If youre talking about specialists, you need to build schools. Each school gives +2.5/5/10 specialists per week. Remember that they are an expended resource, you not only need them for building stuff, raising units, and manning ships, but you need them to replenish casualties too, including from disease/exposure so you can easily run into a situation where you have a net negative of specialists each week if you dont build enough schools.

If you're talking about officers that command units and do regional operations like loyalty or construction boosts, that's different;

Every week when the game changes over from sunday to monday, it does a check. If you have ZERO unassigned land OR naval officers, it will generate a research item in the HQ to recruit either 1 good, 2 average, or 3 newb officers for either land or sea, whichever you have none of, and then you must assign that item to a staff member to research and then wait a few days (theyre really short items) or spend some rep to finish it today. If you have even one officer available to be assigned at the time the game does its check it will not generate the research item in HQ. There is no way to speed this process up, every week you get the chance to unlock 1-3 new officers. You can semi cheese the system by recruiting units with 1 company to cheaply use them up, or by assigning them to region missions, and thus have zero when it does the check every week, but if you miss out on a week thats it, you dont get another chance for more officers until the next monday and it can quickly get VERY expensive having all those officers assigned to doing stuff so you can get more.

Now, if you are talking about generals, you need to unlock more general slots from the commander branch of the HQ research (for the us at least, havent played the brit campaign yet). Look for items that say +1 generals limit. There is a limit to what you can do to speed up getting these. If you invest in doing the 3 items that improve research speed before you set about unlocking stuff, you will have to contend with waiting longer to get things like fusiliers and skirmishers initially, but you will unlock tech MUCH faster subsequently. You can be done with the entire tree by mid 1778 if you can survive investing in research speed early. You can get up to 5 general slots max and the officers you unlock to be generals can ONLY be generals. Do not get these men killed or captured. While there are more than 5 generals you can unlock, these men are the only ones you get so if you get enough of them killed you will be permanently reduced to less than 5 generals. Captured generals can be rescued by taking the location where they are held or in prisoner swaps.