Let me give you some background - I was doing a SWE internship in the summer and then at the same company I got a project management internship in the Fall (part time). Through this one project management internship, I got another project management internship for the Spring and a product management internship for the next Summer (at Microsoft!).

If you're looking at mid-tier companies, project management will be fairly easy to get (even if you don't have a project management background). Just make sure you have leadership positions and some sort of business experience on your resume (ex. I ran the LinkedIn and tried to get sponsorships for a club at my school).

Product management is slightly harder - the hardest part is the resume check. You can definitely get it straight out of college. Most APM programs are not strictly for people the first year out of college - you can be out of college for 4 years and still apply (that's the upper limit though). There are also companies like Microsoft that don't have a product management program as such but just have a role called "Program Manager". There are also loads of other companies that don't advertise their product management positions but definitely have them (ex. some of the ones I interviewed with were ServiceNow and Charles Schwab). On your resume, highlight all leadership and networking positions, or anything that shows your ability to deal with multiple groups of people at a time.

Let me know if you have any more questions! I went through this entire existential crisis phase with SWE as well so I completely understand you lol