Two major things in my favor: I absolutely love the science of sound, and I found a mentor while I was still in college.
I started in car audio because I always lived in someone else's house and couldn't put speakers and wires in the living room wherever I wanted. When I had my first car I quickly realized I could do anything I wanted with speakers so it became my laboratory. Car audio was how I experimented and learned and grew, and I soon found there was a whole community of people who loved car audio too. I joined a couple forums and started making friends.
A big breakthrough was taking the judge training for MECA sound quality competition and then becoming an active judge. This further trained my ears to listen for things, and trained my mind to communicate what I was hearing into a score rubric or into plain words that a non-competitor could easily understand. Becoming a judge is the second-most important thing I've done to further my career because it gave me a new network of people to interact with which is where the first-most important thing happened: I met my mentor.
My mentor has helped me find many ways to connect with the professional audio community, starting with the ALMA organization
https://almaint.org/
ALMA puts on an annual conference where all the engineers at all the serious audio companies come together to talk about all the cool stuff they're working on and the things they learned. This is a place to share knowledge and help eachother. There is some business that happens which is also a draw for professionals already in the field but the best part is the people staffing the company booths are literally the engineers who created the products. If you have a question about microphones, engineers from GRAS and PCB are there to help. If you want to learn about Beryllium as a tweeter dome material, Materion's engineers are there. Wolfgang Klippel is always there and usually brings a few of his employees and they always present something amazing.
Professional networking is something I always shrugged off as "yeah ok that's what old people do" but when I found the right group of people to talk to (the people at ALMA's events) then I realized it was actually amazing. This is where I met Seigfried Linkwitz (from the Linkwitz-Riley crossover) and he invited me to his home to audition his personal audio system where I immediately bought plans to build my own. This is where I met Wolfgang Klippel whom I later had a short internship with at his company in Germany. This is where I met Jerry McNutt who is the head engineer at Eminence Speaker Company where I had a summer internship and was later hired and I began my acoustics career. This is a magical place for someone like you and me.
The neat thing is ALMA's event is virtual this year and admission is free if you register here:
https://almaint.org/elementor-6293/
I cannot recommend this highly enough. ALMA also has a student initiative which is getting stronger. Send me a private message here with your email address and I'll introduce you to Barry Vogel who runs ALMA.
As for starting work after college or going to grad school, I can only tell you what works well for me. I've had a lot of practical experience with audio and a lot of self-taught acoustic knowledge. When I graduated I was ready to never be in school ever again, I hated it with a burning rage I cannot put into words. I ran full speed to Kentucky to work at Eminence and never looked back.
Then I did something unfathomable that I still can't believe: I started grad school. I have been a terrible student on paper my whole life and I'm routinely in the 2.0 GPA range. I have a 3.7 in grad school right now and I'm on track to get another A with my current class. I'm enrolled in the "world campus" at Penn State and taking one class a semester with their distance education program (before distance education was cool like today haha). My company is reimbursing the tuition and I'm learning the most amazing stuff and my favorite part is I'm applying the knowledge in a very serious way before the final exam. Right now I'm taking the 2nd of the signal processing classes and I'm applying literally everything I know in that class to a project this week. It's incredible.
So for me, the combination of practical knowledge and experience with acoustics was powerful and let me start my career. If you don't have as much, you might benefit from grad school and if you go full time then you can get it done in a year or two instead of the 5-year pace that I'm at. Plus you don't have to worry about homework for the next five years while you're also working full time (that part sucks hard).
I guess my advice is do what you love and find two communities: a casual one to make friends and a professional one to start a career (and also make friends). ALMA is the best professional one I know of, so lets start there. Send me a message with your contact info.