It's frustrating to land and see no signal. The good news: nearly every case comes down to a handful of settings. Go through them in this order and test after each one.
1. Is the eSIM turned on?
In your phone's SIM or mobile settings, make sure the travel line is switched on.
2. Is it chosen for mobile data?
Your phone uses one line for data at a time. Choose the travel eSIM under mobile data, otherwise the phone keeps trying your home line.
3. Is data roaming on for the eSIM?
Travel eSIMs connect as roaming lines, so data roaming must be on for that line. It's included in your plan; turn it off for your home line instead.
4. Restart, or toggle airplane mode
A restart makes the phone search for networks again. Airplane mode on and off does the same faster.
5. Pick a network by hand
Turn off automatic network selection, wait for the list and choose another network. Some phones settle on a network the plan doesn't use.
6. Check the APN
Most phones set it automatically. If your email lists an APN, open the mobile data network settings for the travel line and enter it exactly.
7. Are you inside the coverage area?
Check that the country you're in is on your plan's list. A country plan doesn't work across the border; a regional plan might.