Help with Direct Mailing Services?

I’m having a show/event at my place of work where an artist will be there for a meet and greet. I was given around 4K postcards to send out to our client base, however postage is very costly and I’ve recently been told about “Direct Mailing Services”. When I’ve looked up different services such as CactusMail, I keep seeing that they print the cards for me and then send them out. Is there any such service where I can send them my printed material and then they can just send that out? I’m in a bit of a time crunch so the faster the better! :D