When did reconciliation start?

Answer 1

Since you were not very specific in your question, it is hard to tell what reconciliation you are referring to. God started reconciling man to Himself as soon as Adam sinned. God make them coats of skins, which was a way of teaching them that blood must be shed to erase sin. Then they were later taught to sacrifice animals to God, then later Jesus came as our sacrifice for our sins.

Catholic Answer:

The Sacrament of Reconciliation began when Our Lord breathed upon the apostles and said:

"Whose sins you shall forgive, they are forgiven them; and whose sins you shall retain, they are retained." John 20:23

Answer 2

Reconciliation does not have a set starting date, however:

Reconciliation between Indigenous and non-Indigenous Australians is said to have started with the 1967 referendum, where 90% of the population voted in favour of things in the Constitution that discriminated against Indigenous people being removed, this included them being counted in the census.

Since the referendum attitudes towards Indigenous Australians have been changing and National Reconciliation Week began in 1996. Also, Kevin Rudd's official apology on 13th Feb. 2008, was a public declaration of reconciliation.