A common problem for many players is starting slow. Often they have a bad loss or two before they get going, and from there on they play well - but it's too late for that tournament. And this happens over and over. I struggled with it for many years as well - in fact, in my early days, I relied on my serves at the start until the rest of my game came around. If not for my serves, I would have lost the first game to just about everyone competitive. But I solved this problem. Here's how.
The key is both physical and mental. Physically, players do too much robotic warmup, and so aren't ready for real play. Instead, the last few days before a tournament should include lots of random drills and match play, and that prepares you better. Before playing the first match in a tournament, it's also best to play real points to prepare. Everyone's different - when the Hungarians famously upset the Chinese at the 1979 Worlds, I’m told they did two three-hour practice sessions just before the final, back-to-back, with only a short break in between to prepare. But they were in incredible shape. I used to need about an hour to warm up and be at my best.
Mentally, it's a matter of getting yourself into the same mental state you'd be in later on, when "in the zone." Being in the zone isn't anything magical, it's just a matter of focus. Some do this easily; some have to play (and often lose) several matches before getting into it. Instead, as I always tell my students, "Think of the mental state you were in during the best match you've ever played." Then go into the match with that same mentality, for every match you ever play. For me, I spent many years remembering the mentality I had when I beat 2550 player Rey Domingo in 1990, 21-15, 21-14. It was magic – everything seemed in slow motion and I could do no wrong. That's what worked for me when I had to overcome this same problem many years ago and has worked for many others I've coached.
The key is to go into the match able to "play free," where mental and physical overlap. The physical side means letting yourself go and just reacting to an incoming ball. That's why predictable warmups like forehand to forehand or standard footwork drills won't by themselves prepare you for a match - you aren't reacting to an unpredictable ball since you know roughly where the ball is going, and so aren't working on "playing free." Besides playing points (not necessarily games), a great drill to get into this is a standard random drill, such as where your partner blocks to all parts of the table and you just react, FH or BH, like in a game, except keeping it to one side, either forehand or backhand. This allows a player to get into "playing free."
It's also good to have a code word or phrase that you tell yourself, that helps signal your subconscious that it's time to play. I always feel a bit sluggish early on, and so mine has always been simply "push yourself." I would say this to myself between points as I walked about, and it worked, both physically and mentally.