Not every manager can sign. The certifying executive must be an owner of the company (only if it is a sole proprietorship or partnership), an officer of the corporation, the highest-ranking company official working at the establishment, or the immediate supervisor of that official. A safety manager can prepare the summary but usually cannot certify it.
Because the executive is attesting to a process, the useful question before signing is how the log was built: who reviewed each case, how outcomes were confirmed, and where the hours worked and average employee figures came from. If you use an equivalent form instead of the OSHA 300A, it must still include the employee access and employer penalty statements. The guides here cover who signs, a certification checklist, the packet an executive should review, and those required statements.