Hi, I've been a SLPA for 5 years in CA. I did not follow the steps that the previous person stated.
I received a bachelor's in Speech-Language Hearing Science in Pennsylvania, and the hours which I received through my undergraduate program were enough for me to become certified. However, CA has increased their hours to 100. TYou can simply reach out to pediatric clinics in your area and explain that you are looking for 75 more hours of fieldwork experience to become a licensed SLPA. You can present the application to them which is listed on the website you provided in your post. In this case, a SLP from the clinic will be asked to take on a student (this would be you) for X amount of time.
Once you have completed the hours, you can apply for the SLPA license. The process will take anywhere from 1 to 3 months depending on other applications at this time. Once you receive the license and license number, you can simply apply to SLPA jobs in the state that you are licensed (in your case CA). The company you interview for will always have a supervisor SLP ready to take you on. You don't just need to convince someone to be your supervisor - there is already a system for this which SLPs must adhere to (check ASHA website for more information on SLP supervision requirements). You should always ask questions about what your supervisor will expect from you in your interview to ensure that they have a supervision system in place. There is also a supervision form which you will need to submit to your state once you have accepted a position including your signature and your supervisor's signature. This is very important.
Please let me know if you need any links!
Good luck!