When Lord Vishnu took human avataras like Vamana and Krishna, He appeared in chaturbhuja form holding chakra, shankha, gada and padma along with all ornaments and Shrivatsa mark on His chest. This description for Vamana avatara is found in Bhagavatha Purana Canto 8 and that for Krishna is also found in Bhagavatha Purana Canto 10. Rama is also a human avatara of Lord Vishnu. Did Rama also appear in chaturbhuja form like Vamana and Krishna at the time of His birth?
The verses for birth in Tulsidas Ramayan are:
भये प्रगट कृपाला दीनदयाला कौसल्या हितकारी।हरषित महतारी मुनि मन हारी अद्भुत रूप बिचारी॥१॥
लोचन अभिरामा तनु घनस्यामा निज आयुध भुज चारी। भूषन बनमाला नयन बिसाला सोभासिंधु खरारी॥२॥
निज आयुध भुज चारी translates to holding weapons in his 4 bhujas. So according to that version, Lord Ram did indeed appear in Chaturbhuj form.
Later the verses say
सुनि बचन सुजाना रोदन ठाना होइ बालक सुरभूपा। यह चरित जे गावहिं हरिपद पावहिं ते न परहिं भवकूपा॥८॥
which means the lord changed form to a crying child after Kaushalya requested him to.