Appears that Margate was in Thanet union, so:
https://www.workhouses.org.uk/Thanet/Kent History and Library centre hold workhouse records + board of guardians records including a register of deserted children, admission/discharge records for cottage homes if he was placed there before fostering out, etc. Luckily it looks like quite a lot of records survive; in some areas there's basically nothing.
If they don't do direct research + you can't get there, you can probably find a local genealogist with an hourly rate who can go for you.
