[Machine] I saw the Prophet ﷺ do that, and we have narrated from the hadith of Al-Mas'oodi from Ziyad bin 'Alaqa from Al-Mughirah bin Shu'bah something similar, and the Hadith of Ibn Buhaynah about prostration before the greeting is more authentic than that, and Allah knows best.
رَأَيْتُ النَّبِيَّ ﷺ يَصْنَعُ ذَلِكَ وَقَدْ رُوِّينَا مِنْ حَدِيثِ الْمَسْعُودِيِّ عَنْ زِيَادِ بْنِ عِلَاقَةَ عَنِ الْمُغِيرَةِ بْنِ شُعْبَةَ مِثْلَهُ وَحَدِيثُ ابْنِ بُحَيْنَةَ فِي السُّجُودِ قَبْلَ السَّلَامِ أَصَحُّ مِنْ ذَلِكَ وَاللهُ أَعْلَمُ