Back in the day when babies used to sleep on their tummies crawling actually DID happen sooner. Now we have to carve out "tummy time" for babies who sleep on their backs and many freak out when placed on their tummies.
Yes, I would institute more tummy time. Make it fun for both of you, lie on the floor (or bed) at eye level with him and talk to him. Then use a toy to entice him to crawl. My babies all crawled at different ages, my oldest didn't crawl until 8 months, but she loved to sit and play at that age. My middle one was about 6-7 months, and she had a really chubby belly to get over to get into a crawling position. We worked with this for a while, as she would get half way over her belly and give up. My youngest (my preterm baby) was crawling before 5 months. She was so small and light that she was able to pull her entire body weight really young. She was also very motivated to get moving. She was my busiest baby! Always looking for paper to tear up and chew, VCR tapes to unravel, getting the velcro on her Papa's sandals to open and close them over and over again. (Yes. DH is a big nerd. He wears velcro close sandals.)
There are some theories that crawling with cross motion of arms and legs facilitates language learning. I do think it's important for babies to crawl. Some kids skip that step and go right to walking, but these tend to be early walkers.