Today, you can start your CPF payouts at any time from age 65. There is no link to the current retirement age of 62 or the re-employment age of 67. Even if the retirement age and the re-employment age are raised, the CPF payout eligibility age would remain unchanged.

For more info:

Information on the CPF Payout Eligibility Age (RSS) (CPF LIFE)

Information on the retirement and re-employment ages