The airman, from Dunfermline in Fife, disappeared while on a night out in Bury St Edmunds, Suffolk, in September.
A bin lorry collected refuse a short time later from the area the RAF Honington gunner was last seen.
Suffolk Police said officers were trawling through 60 tonnes a day at the site in Milton, near Cambridge.
The search is now in its third week and is expected to take up to 10.
A team of eight trained search officers is searching more than 920 sq m (1,100 sq yd) of waste to a depth of 8m (26ft) and has trawled through 845 tonnes so far.
Despite earlier claims, the force said the decision to search the site was not prompted by data provided by an intelligence firm, hired by Mr Mckeague's family.
Mr Mckeague's mother Nicola Urquhart brought in McKenzie Intelligence Services after she expressed concerns with the police investigation.
Its managing director Forbes McKenzie said data provided about Mr Mckeague may have helped direct police to the landfill site.
But, police said they had planned to search the site before it was revealed a bin collected from the area where Mr Mckeague was last seen was heavier than first thought.
A spokeswoman said: "Officers have been liaising with the company that provided the [bin weight] data to check and re-check the information provided.
"This has involved them going back through thousands of lines of raw data to check the information, leading to the error being found.
"This was not in any way linked to data provided by MIS, the private company employed by Nicola Urquhart."
Mr Mckeague, 23, was last seen at about 03:25 BST on 24 September.
Police seized a bin lorry in the early stages of the investigation, but no traces of Mr Mckeague were found in the vehicle and the landfill site was not searched at the time.
Its route appeared to coincide with the movements of Mr Mckeague's mobile phone.
Detectives searching for missing airman Corrie Mckeague have sifted through more than 800 tonnes of rubbish at a landfill site.