Vanguard Research actually wrote a paper about this called 'Dollar-cost averaging just means taking risk later' [0].
Or if you would like more recent research the paper 'Dollar Cost Averaging v.s. Lump Sum Investing' by Ben Felix [1] is worth a read imho.
0: https://www.passiveinvestingaustralia.com/wp-content/uploads...
1: https://www.pwlcapital.com/wp-content/uploads/2020/07/Dollar...
Edit: Formatting