Underpaying a new engineer doesn't solve anything. It's honestly just shortsighted laziness or already having a staff of engineers who aren't good enough at their craft or communication to be good teachers.
If you're paying someone $1000/week you're paying them $50k per year and by your staircase approach you save.... one weeks worth of salary or 2% of the first year which ends up just being an insult to the new engineer and unnecessarily making their lives harder taking money out of their pocket when they need it most (getting a new job having not had a job or having to switch with the gap in income)