Academic Probation on Transcript- Chances of Being Accepted as a Transfer?

Hi!
I am a freshman and have recently completed my first semester in college (Fall 2019) and am in my second semester (Spring 2020). My first semester in college was pretty rough for personal reasons and the results are very evident in my grades and GPA, so much so that I was placed on Academic Probation. This will show up on my transcript. My GPA, as of right now having completed 1 semester, is a 1.8. My university, thankfully, has a “freshman forgiveness” program in which I can retake two courses taken during my freshman year and those grades will replace the original.
I am doing MUCH better this semester- I am a lot more focused, motivated, and responsible. I have so far not dipped below an A in my classes (though it is still early in the semester). I am typically a very strong student, however in my first semester I simply just had a lot of external things to deal with. I also plan on taking summer courses in order to continue to bring up my GPA.
Anyways, I am considering transferring schools for many reasons, definitely no sooner than after my junior year. I am really interested in going out to California and specifically looking at some of the UCs. I am worried, however, that with my academic probation being recorded on my transcript, I will have no chance at transferring to a good school, even if I bring up my GPA to my goal (3.5 or higher). This is starting to give me some considerable amount of anxiety! Any honest thoughts will be of much help. Specifically for California schools, such as USC, but also for any good school in general… Do I have a REALISTIC chance? If so, what are some things I should be doing that I may not have considered?
All the help I can get will be very, very appreciated. Thank you!

If you apply to publics in California, like the UCs/ CSU’s, you will be paying non-resident tuition. There is no financial aid for non-residents. UC’s will cost you $65K per year. CSU’s about $45K per. Remember that there is NO funding.

USC is a private university and a non-public. Cost of attendance runs about $72K+. Is this affordable for your family?

California schools are very competitive and impacted. Depending on your major, your GPA has to be BETTER than the instate students, if you want a chance of getting in. GPA should be closer to 4.0 for consideration.

They won’t care about academic probation if the current school attended is fine. The only exception is if the probation is from a UC. If so, the GPA needs to be resolved with other UC courses, including UC extension.

“I am really interested in going-out to California.”

Meaning out of state? It costs around $60k a year to go to school in CA from out of state. That’s a pretty big stretch, even for the well-to-do. Are your parents willing to pay that kind of money for tuition and the atrociously high cost of living? That’s the only way you’ll be able to go out there.