If CSQ goes successfully, then you can proceed with PR and
yes I understand, but you dont have a valid work permit and you are working full-time only because of special policy.
LMIA is a pre-work permit time consuming process and most employers dont engage in headache immigration matters.
After you guys have a CSQ, the quickest you can do is following (If you dont want or dont have all the document ready for PR)
1. Your husband can ask his employer to get a an offer of employment number which employer can do without the LMIA (this option is only for main CSQ applicant)
2. Once he gets this employement number, he can apply for employer-specific WP. See following link
https://www.canada.ca/en/immigratio...t-market-impact-assessment-exemptions.html#t2
3. At the time he applies for employer-specific WP, he can apply for your OWP using Family members of WP holders who are Economic Class PR applicants or chosen by a province [R205(c)(ii) – C49]
https://www.canada.ca/en/immigratio...ublic-policy-competitiveness-economy/c49.html