H-1B to EB-1A
H-1B is a temporary work status. EB-1A is a green-card category. Holding H-1B does not help or hurt the ten criteria. The work you did while on H-1B might.
The employer does not have to sponsor EB-1A
EB-1A does not require a job offer or a labor certification. You can self-petition. Your H-1B employer can still be the distinguished organization in a critical-role argument. That is about the work, not about who signs the I-140.
Whether you should stay on H-1B, change status, or travel while a petition is pending is a lawyer question. This site does not answer it.
What to evaluate instead
Ignore the visa stamp for a moment. Paste the resume, or answer the eight questions on the EB-1A guide. See which of the ten criteria are claims and which have exhibits. If the file is only the H-1B job description, it is early, whether or not the employer is famous.
The searches that sit next to this one
Most H-1B readers are engineers, often chargeable to India. The job title is not the case. Original contributions, judging, a critical role, and sometimes scholarly articles are. A citation total is not a USCIS cutoff. If the acclaim file is thin, NIW is a different test, not a discount version of EB-1A.
Related: EB-1A guide, Self-petition, EB-1A vs PERM, Critical role, Software engineers.
EB-1A guide: the 10 criteria, the petition, and India
This is not a law firm and does not file petitions. USCIS decides each case on its own record.