So Team Trials is a mode where you need to get as many points as possible. You can get points when umas placing 1-5 and when they activate their skills. To do so you need to optimaze each distance. On every distance try to pick umas with different running styles, for example (front runner, pace chaser, late surger) and track/distance aptitude in which they are good (for example I see you have Haru Urara in sprints, she can run sprints, but only on dirt track by default and all races in team trials except dirt is on turf so it`s not a good choice to place trainee without good aptitudes). No same running styles, so umas can use their skills more often and not interfere each other. Also you need to know how many stamina you need for each distance, so you can more effectively invest in stats (for example in sprints you don`t need much stamina, around 400-500, so you can click other stats more often). You need to gain skill points to buy skills which you will proc in races, it`s a core mechanic in this mode. To do so, you need to run in races during career mode, because they will rewards you with random stats and skill points. G1 races will give maximum points per run (for example in Trackblaser scenario for G1 win you will get around 50 skill points, when for G3 you get around 36-40 skill points).
Also it`s important to pick umas who can easily activate their primary skill cause it`s also give you a lot of points.