It depends on how far away the colony was.
The First Fleet (to establish the British penal colony in New South Wales) left Portsmouth on 13 May 1787. En route they stopped at Tenerife (3 June 1787), Rio de Janiero (5 August 1787) and Cape Town (13 October 1787), and presumably word that they had made it to these places in due course got back to Britain. The 11 ships of the fleet arrived at Botany Bay on 18, 19 and 20 January 1788.
On 24 January 1787 two French ships arrived at Botany Bay; those ships sailed on 10 March 1787, but never made it back to Europe; they were shipwrecked in the vicinity of Vanuatu. So this contact did not result in word of the First Fleet’s safe arrival getting back to Britain.
In fact, confirmation of safe arrival did not get back to Britain until the Prince of Wales, one of the First Fleet vessels, arrived back in Falmouth on 25 March, 1789, more than twenty-two months after the fleet had first sailed.