Can a cell make a protein directly from a gene?

Yes it can come from a gene

The journey from gene to protein is complex and tightly controlled within each cell. The type of RNA that contains the information for making a protein is called messenger RNA (mRNA) because it carries the information, or message, from the DNA out of the nucleus into the cytoplas. Each gene tells the cell how to put together the building blocks for one specific protein. However, the gene (DNA) sits inside a different compartment of the cell (the nucleus) from the location of the cellular machines that make proteins (ribosomes). So I'm gonna go with yes.