The DFARS clause 252.204-7021, Contractor Compliance with the Cybersecurity Maturity Model Certification (CMMC) Program, requires compliance with the CMMC Program. Your prime contractor is required to flow down clauses that apply to the subcontractor's portion of the work, but whether CMMC applies to your specific scope depends on the type of information you will be handling and the CMMC level specified in the prime contract.
CMMC Level 1 is a self-assessment and applies to contractors who handle Federal Contract Information (FCI). FCI is information not intended for public release, provided by or generated for the Government under a contract. If your work involves accessing or processing FCI, then CMMC Level 1 would apply. If you will not be handling any FCI, then the CMMC requirement would not apply to your subcontract.
You can review the prime contract's Section L and Section M to understand the specific CMMC requirements for the overall contract. The contracting officer is the ultimate authority on what clauses apply. You should communicate directly with your prime contractor and request clarification on the specific data types you will be handling and the justification for the CMMC flowdown to your firm, citing your role as a general construction sub that does not handle technical data or Controlled Unclassified Information (CUI).