Am I too late in the game?

Few years removed from the SA recruiting mess, but my two cents

It will be difficult to get in as an SA to BB/EB, but not impossible, will just require a lot of networking and luck. I would apply ASAP - cover letters don't matter very much, would just have a generic one and make sure you get the bank name right. Typically, I would have a generic intro, and then namedrop that I had conversations with employees x, y, and z, and their deal experience made me want to apply or something like that. Much more important to network and get an internal referral. Once you get on the phone with someone (you will eventually), try and get them to refer you to HR and both another banker at the firm. IMO should focus most of your efforts on networking vs. technical prep for now - getting the interview is the most difficult / important thing in the SA process (although of course should still do some interview prep)

It is definitely easier to work for a regional bank or other boutique that has a decent brand name and lateral upmarket as a full time, if that's what you want to do and you're willing to put work in to lateral. Probably easier in the past to lateral as an SA with an offer in hand, especially given current crappy market. More likely you'll have to do a full year at wherever you SA, then lateral. Anyway, I personally thought lateralling was easier than getting an SA job, it was just a matter of knowing the right person to refer you for the open spot. Interview questions asked were typical similar to SA super day questions, which after a year on the desk as an FT you should probably just know via work experience. Also thought that laterals were generally stronger than most SAs who converted to FT, and I know wasn't alone in that opinion.

To my second point, I can't stress this enough, Networking is absolutely everything, and it is a numbers game. Typically folks from non traditional paths or non targets are more receptive to cold emails from folks from similar backgrounds and are more likely to push for you internally if they think you're good. Target school kids usually have enough on their plate with their schools already, and the process for their schools is so well-defined, they don't need to go above and beyond to help someone get a job.

Some other networking tips I thought were helpful: 1) Don't be afraid to reach out to senior people. MDs have a surprisingly high response rate, and if they like you, you are guaranteed an interview. Just make sure you ask good questions about their industry and big picture questions in general. 2) Ask good questions - don't ask stuff like what is process like, what is timeline, what's culture, etc. Everyone asks that. Ask an analyst to refer you to HR and you can ask them that (also can be direct and ask them how to maximize chances of getting an interview - typically HR folks are pretty nice/normal and want to help out). Ask analysts questions about their industry/deals, and try and be spontaneous - it's really impressive (and rare) when a candidate asks smart, thoughtful unique questions about the nuances of a deal or industry that shows they're curious and actually like finance and want to learn. 3) This is not for everyone, but it doesn't hurt to specialize. It was helpful for me in my recruiting process, as I focused 75% of my time on going after a niche industry not many folks wanted. Helped me stand out from others - everyone wants TMT, Fintech, Consumer, etc. I actually botched one of my superday interviews, but the industry team really liked me and pushed for me, so I got the job anyway. Would only do this if you either really liked an industry, or were OK with going into a niche area.
 

Overall, as I'm sure you've seen, banking is not a "difficult" job. Breaking in is the hardest part for most folks, but there are always opportunities out there. If you are smart enough, normal enough, and motivated you will be able to find a very good gig.