What other ways can you file when married? Jointly we do not qualify for EIC is there another way to file?

The only other way to file is Married filing Separate.  But you can’t get the EIC if you file MFS.  You could file Head of Household if you lived apart from your spouse the last 6 months of the year and have a qualifying child or dependent.

Some EIC articles

IRS- Earned Income Tax Credit info

https://www.irs.gov/Credits-&-Deductions/Individuals/Earned-Income-Tax-Credit

Turbo Tax EIC INFO

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-credits-deductions/earned-income-credit-eic-affect-refund/L4SKPikAa_US_en_US

You can get the EIC without a dependent

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-credits-deductions/qualifications-earned-income-credit-eic-eitc/L7w4BFP32_US_en_US