Generally in CA, non-compete contracts aren't enforceable, and employees are free tp change jobs, start their own businesses to compete with former employers, etc. Exceptions to this general rule are when someone sells a company to someone else --then, they can't compete with their buyer.
There are enforceable contracts protecting trade secrets, and contracts which prevent solicitation, which is what I think you mean by "poaching."
Here, if you didn't sign any contract (and didn't sell any company to anyone), then there's no restriction on you. As for what enforceable restrictions there might be on Company B, they'll need to have their own lawyer review their contract with Company A. If Company B hires you, they might ask you to indemnify them (pay their legal expenses) if Company A sues them because of you, in which case you'll need to own business/employment lawyer.
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I don't know how you would know about the "no poaching" agreement between Company A and Company B [generally referred to as a "no solicitation agreement"]. But assuming there is one, and its operative and enforceable, then if Company B solicited you to join the company, and therefore leave Company A, that would breach the no solicitation agreement. Where it gets squirrely is if YOU approached Company B and asked for a job. To evaluate if Company B violates the no solicitation agreement in that situation [because it benefits from what you've learned at Company A] requires an analysis of the terms of the provision -- they are not all the same. You need to speak with a California-licensed employment attorney.
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You must mean "poaching" not "pouching". A "non-poaching" agreement is an agreement that the companies will not try to steal each other's employees.
It is not up to you to prove anything because you are not a party to the agreement, unless they had you acknowledge it, in which case your acknowledgment will be interpreted as a non-compete clause attempting to restrict you from switching from A to B in response to any inquiry from B to you. Whether, and to what extent, such a restriction is legal is a matter of CA law and I am not licensed in CA so I cannot advise you.
As to how you prove you were not approached by B, you can do so by merely so stating, preferably under oath, such as in an affidavit signed by a notary. If you wanted to tie this up further, you would have an authorized knowledgeable representative of B sign an affidavit that B did not solicit you but rather you solicited them. Once you affirm you were not solicited, it is up to A to prove you are lieing and you were solicited, which is next to impossible because the only proof is likely to be in the possession of you and B unknown to A. A might have to find an employee of B to testify, whether truthfully or not, that B solicited you. You should plan for the worst, namely that A can find someone disloyal at B to throw you under the bus, and document as well as you in each piece of correspondence with B each step of the way that YOU asked B for a job and not vice versa.
California looks with disfavor on non-compete and non-solicitation agreements, so you need to see a California-licensed employment law attorney to confirm or correct the above information.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.