With my Edge 1000, I turn it on as I'm leaving my garage and it's nearly always got satellite lock by the time I've reached the end of my driveway. With the 1030, I turn it on as I'm leaving the garage, and more often than not I'm a kilometre or more down the road before it finds the satellites. If I wait for it to get the satellites before I roll off, I'm waiting 2-3 minutes.
You've got a problem then. Just out of curiosity, I went into my garage where my 1030 is connected to my bike on a trainer. Turned it on and changed to road mode. Connected to the satellites in 30 seconds or less. That was INSIDE my garage.
Irrespective of the fact that you got lock earlier when moving with the 1000, as a matter of course you should always wait to get satellite lock before moving off. Not sure if there is an EPO.bin file in the 1030, but this file needs updating on a regular basis. That file contains the satellite ephemeris data and requires regular updating. This happens when you connect to a computer via Garmin Express. Read this - https://www.dcrainmaker.com/2016/03/why-your-garmin-gps-is-better-off-taking-epo.html
My 1030 gets connected to the PC and Garmin Express every couple of days when I charge it. The last time before this morning's ride would have been the day before yesterday. It was connected again today - I just checked and the EPO.BIN file is dated today.
If you are having problems gaining satellite lock when stationary in an open space before moving off, and you are certain your EPO.bin file is up to date, then you should contact Garmin Support.