In the name of Allah, the most Beneficent, the most Merciful.
Saaiduan Abu Qatadah Radiallahu Anhu narrates that the Prophet of Allah Sallallahu Alahi Wasalam has said; “When one of you enters the masjid, then let him not sit until he prays two rakaats.” (Sahih Bukhari p.63 v.1)
Saaiduna Abu Dhar Radiallahu Anhu has said: “I entered the mosque, and there was the Prophet of Allah Sallallahu Alahi Wasalm sitting alone, so he said: ‘Oh Abu Dhar, Truly the mosque has a greeting, and indeed its greeting is two rakats, so stand up and pray them.’ (Sahih Ibn Hiban)
In the Hanafi Fiqh, if a person was to sit down and then stand up and read his tahiyatul masjid, he will still get the same reward and it will not decrease by sitting down. (Raddul Muhtar p.460 v.2)
With regards to your question there is nothing wrong in giving salaam before starting the tahiyatul masjid and giving salaam will not decrease a persons reward.
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham