What should I do when I can't get any construction employer to call me back when looking for a job?

All you can do is attempt to reach the construction employer and submit your construction resume and interest. You should try to send your construction resume to the appropriate contact listed in the job posting, or attempt to reach out directly and indirection (networking) to the construction HR department or operations department head. If you do not get a response you can continue to resubmit your credentials until you do. However it is common for construction employers to not get back with construction applicants, especially if the construction employer does not have an established construction HR department to process applications.