Is there a setting to increase the tie length at the start of a new system. I could not find such so far. I often get this:
There was a thread about this from 2019. I am hoping there may be a way now?
Nope. Fairly frequently I find myself resorting to Note Spacing mode to fix these manually.
Sub-optimal behaviour from Dorico. 
What sort of note spacing change do you make to address this? Nothing I did makes any difference. Can you explain?
Leo possibly means manual note spacing . Add a little space before that first column; works fine with minimal tweaking.