"Soft fired" as part of firm cuts

Based on the fact that you have a few months to secure a role, I assume you will technically still be employed by the firm for the next few months. This means you have the great luck to start recruiting intensely for another position without any real problems (at least on the outside). Your potential employers will have no idea what actually happened to you for the next few months. Having to explain why you were let go or resigned from your firm suddenly would be a lot harder and more stressful.

If you have been at the firm for more than a year or so, you have the advantage of positioning your story as someone who didn't enjoy his or her experience at the firm (one year is enough time for it to make sense). You should ideally have some concrete reasons why and how working at the firms you will be interviewing at will help to resolve those problems you were having. Considering you're at a BB, it might be easier for you to lateral to an EB or MM so you can emphasize the disadvantages of being at a BB and how you realized you enjoyed the advantages of EBs/MMs (like leaner deal teams, closer client interaction, etc.). Ironically, the more you talk about how other banks would provide you with better opportunities and experience, the more you will believe it and want to disassociate yourself from the firm anyways. Given everyone in banking and finance knows about your firm's financial condition, it will be much easier for you to lateral as well. If you think you can convey in a convincing way to other BBs that you are very hesitant about the future of your struggling BB, then go for it.

Look at online job aggregators like LinkedIn, Indeed.com, etc. for open analyst positions. Then, reach out to someone on the team and ask to talk about the position. Because they are looking for someone, you should easily be able to have an interview set up (assuming your resume looks good and you present yourself well in intro conversations). You should also reach out to as many of groups/banks as you can (either through friends or cold emails) to see if there is an open position. Perhaps you get lucky and thrown into an internal process for an analyst position that the firm has not yet posted online (or might never end up doing due to the amount of candidates they already have for the position). Note that it's much easier to switch within the same industry group.

Be very thankful you were soft fired. You have a lot more time to secure a new role now compared to normally being kicked out without notice and scrambling. Bigger firms usually don't have any type of soft firing and will just suddenly show you the door. You have provided a lot of great advice on this forum for which I am very thankful for. It's obvious you're a smart and mature guy so it will be pretty easy for someone like you to find an awesome job!