I went to a technical high school and was in Carpentry as well. It seemed so rewarding to actually make something and see that finished product after.
I would check with the school and the job core reps to see if they have contacts for an entry level job with a carpenter. The way to start is to simply get out there and work with someone. The good thing about Carpentry as a trade is that there is so many different things you can do.
There is finish carpentry, rough framing, cabinet making, even working with and building concrete forms.
I would say your best bet is to try and find a part time job working with a carpenter and do not be afraid to try different aspects of the trade.
Hope this helps
San Jose job core should have some counselors or resources to connect you with people in the trade of your interest. Reach out to them and you can also reach out to friends and family to see if they know anyone that you can connect with. If these options don't work just find a shop near you that does work that interests you. Go by and ask if they are looking for any apprentices. And don't be afraid to try different things. My family is full of tradesman and they have done many different types of jobs until they found the one that they felt the most passionate about. And remember no matter what job you end up doing, always put safety first! It's not worth it to cut corners! Good luck to you!
I would suggest to define your craft, there are many specialties in this field.
Designer (furniture, Norastructure, frame design)
Finish carpenter (mostly in construction heavy math calculations are required)
Once you have identified your field! Then I suggest you start an apprenticeship process. I build homes and I hire all kinds of carpenters, from the ones that make cabinetry, design and finish work on a multiple level of artisan craftsmanship, included construction workers building frames! To stairways, closets! So much… to furniture design
I wish you the very best in your career!!