The Tiger 1050 as with many other Triumphs has issues when attempting to start from cold, this problem is normally due to a connection problem in the electrics or more specifically the starter motor.
Check all the connections, then take them apart and clean them? They can look perfectly fine from the outside, but when you take them apart and look at the mating surfaces, they can be glazed over. Most common problems are battery or connections. Take all connections in the path from the battery + to the starter, the starter to ground (if there is a cable for that. I don’t really know on this bike.) and from the battery – to ground apart and clean all the contacting surfaces with a wire brush, or sandpaper, or scrape with a knife blade until you have clean shiny metal to metal contact.
It is not uncommon to find paint under ground connections that are attached to frames. If that does not cure your problem, then start in with a voltmeter. Measure the positive voltage at the battery when trying to start the bike. (note this value as you may need it later.) I would not expect it to drop lower than 10.5 to 11 volts. If it drops lower, try adding another battery using jumper cables. If the bike starts then, your new battery is probably defective. I’d take it to an auto parts store and have them test it under load. Still no joy? You have a current path from the positive battery terminal to the solenoid (which may be built onto the starter motor) to the starter motor to ground. All of the voltage drop should be across the starter motor. If there is a drop anywhere else in that path, that is the problem. Measure the voltage at the positive connection on the starter while starting. It should be the same as at the battery. If it is lower, the problem has to be between there and the battery and the only things there are cables, connections, and solenoid. If it’s okay, measure the voltage at the starter terminal that is connected to ground if there is one (the starter could be grounded through it’s case to the motor in which case, you can ignore this step). It should be zero. If it isn’t, then the cable from there to ground is bad.
For more details on how to resolve starting problems click here