You're correct that trip IDs are not stable over time, since of course the scheduled service on a line changes over time, which necessitates adding or removing trips.
If you just want to fetch any single valid trip on the Red Line, you can use the `route` filter on the `/trips` endpoint (e.g. /trips?filter[route]=Red&page[limit]=1). Similarly, you can filter the `/schedules` and `/predictions` endpoints by route if you'd like to directly get a stop time for the game without going through trips.
Route IDs are stable over time unless the route itself is eliminated — unlikely, in the case of the Red Line, but if you wanted to avoid hard-coding any specific ID you could request `/routes` and pick one (this endpoint has no required filters).
Hope this helps,