get off to a flying start

get off to a flying start (said of a task, project, etc or of a person: to begin promisingly or with a special advantage) — удачно начать

a flying start (a quick and auspicious beginning) — удачное начало

The Webster suggests 'старт с хода' which sounds odd to me, I'd rather say 'взлет без разгона', but I can't translate this into Russian adequately.

see also
[hit the ground running]