No airport, two road borders: when to switch
Andorra has no airport. Almost everyone arrives by road, by car or by bus from Barcelona or Toulouse, through one of two borders: La Seu d'Urgell on the Spanish side or Pas de la Casa on the French side. That makes the moment to switch easy to plan. Install the eSIM at home over wifi from the QR code in your email. Before the border, set it as your data line and turn on data roaming for it, and leave roaming off on your own SIM.
There is a single mobile network in the country, Andorra Telecom's, and your usual line would join it as a roaming customer on the first stretch of road past the border. With roaming off on that line, it stays quiet. The eSIM's days start at its first connection in Andorra. On the way back down to Spain or France, make your own line the data line again.