I'm having the exact same issue, playing in the UK. The game works fine during the day, but somewhere between 5PM and 7PM GMT it stops working, every day, until about 1AM.
At this point, I can no longer join any matches - I either load into a black screen or get kicked to the main menu with 'connection to server timed out'
I'm on a high-speed VDSL connection with a Netgear Nighthawk router (ie not shabby!), but in frustration I've also tried out two other routers, and tried playing from three other locations (friends' houses, one of which was 20 miles away). No joy. My personal connection is a business line, which has no traffic shaping and highest priority - and I've tried both NAT2 and DMZ connections to ensure no ports are blocked.
Furthermore, I have a library of 30+ PS4 games, and I've never suffered a similar issue with any of them. I've even had parties running FOUR machines playing Battlefield One at the same time.
Several of my friends have had the exact same issue, most of them returned their discs to the retailers for a refund. I bought a digital copy so I seem to be stuck with it.
Please see attached Traceroute screenshot.
The sheer number of people affected and the fact that this only happens with Titanfall 2 really seems to suggest this is a server-side issue.