Praise be to Allah.
There is nothing wrong with congratulating one another at the beginning of the month of Ramadan . The Prophet (peace and blessings of Allah be upon him) used to tell his Companions the good news of the onset of Ramadan, and urge them to make the most of it. Abu Hurayrah (may Allah be pleased with him) said: “The Messenger of Allah (peace and blessings of Allah be upon him) said, ‘There has come to you Ramadan , a blessed month. Allah has made it obligatory on you to fast (this month). During it the gates of Paradise are opened and the gates of Hell are locked, and the devils are chained up. In it, there is a night that is better than a thousand months , and whoever is deprived of its goodness is deprived indeed.’” (Reported by al-Nasai, 4/129; Sahih al-Targhib, 1/490)
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And Allah knows best.