Can we sue for civil compensation after the patent comes first?

You can sue for compensation.

According to the provisions of the Patent Law, the patentee who owns the earlier patent has exclusive rights to the patent, and can bring a civil lawsuit against the patent infringer with the later patent to claim damages. The patentee may bring an infringement lawsuit to the people's court, demanding that the infringer stop the infringement, eliminate the infringement consequences and compensate the losses.