i would go down to a 16 teeth sprocket and see how you go and and get a 11-40 a new chain is a must
When you take your bike to get it sorted out you will need a new lock ring and o ring to put the new front sprocket on
you can buy them offline they are not very expensive about £30 quid for the lock ring at the 16 teeth sprocket plus the chain and the rear cassette and give that a go
Ask the mechanic what it has at the moment and work from theirs but a 16 is a good guide depending on your terrain
if 16 teeth is not enough then just drop down again and then at some point you will find the happy medium to suit your terrain
16T would be raising the gearing, not lowering it.
https://www.cube.eu/uk/products/e-bike-trekking/cross-hybrid/cube-cross-hybrid-pro-400-blacknred-2016/
From the spec above, the Cube Cross Hybrid 400 comes with a 15T as standard, so it would mean changing to a 14T front sprocket, from the standard OE 15T. (If I have the right bike, and the spec is correct)
The rear is also a nine speed 11-34 cassette, so plenty of options to go lower on that. If it were me, I'd leave the 15T front as it is, and just change the rear cassette for either an 11-36 or 11-38. Going much larger with the lowest gear, could possibly then mean a change of rear mech from a medium cage to long cage, or at the minimum necessitate a longer B screw to be fitted, which is no big issue.