Understanding the three Ashara's (Parts) of Ramadaan

One of the prophetic hadith quoted by Islamic Scholars on Ramadaan is that the Messenger of Allah ﷺ said “The first part of the month of Ramadaan is mercy, the middle of it is forgiveness and the end of it is freedom from the Fire.”[1] - The first part is mercy does not mean that the unimaginable immense Mercy of Allah ﷻ is not going to be throughout the remaining Ramadaan. The first part is mercy because everything in the creation begins with the Mercy of Allah ﷻ including Ramadaan ul Mubarak. The first Verse in the Entire Quran begins with His Mercy (Al Quran 1:01) Bismillahir-Rahman ir-Rahim - With the Name of Allah ﷻ The Most Gracious The Most Merciful. The first part is mercy also because Prophet Muhammad ﷺ said "When there comes the month of Ramadan, the gates of mercy are opened, and the gates of Hell are locked and the devils are chained."[2] Which means that the path to hell fire is blocked, except for those who still choose to go on that path. 

Not to forget that beginning of creation happened due to Mercy of Allah ﷻ. Messenger of Allah ﷺ said: "When Allah decreed the Creation He pledged Himself by writing in His book which is laid down with Him: 'My mercy prevails over my wrath.'"[3] Every human was created in their mother's womb due to Mercy of Allah ﷻ: (Al Quran 3:06) It is He Who shapes you in the wombs of your mothers as He wills - The Quran uses the word Arhaam for womb which is derived from Rahm which means Mercy. The arrival of Prophet Muhammad ﷺ as the final messenger for entire creation and the completion of revelation is a great part of His Mercy: (Al Quran 21:107) And We have sent you (O Muhammad) not but as a mercy for the 'Alamin (mankind, jinns and all that exists)

Therefore everything begins with the Mercy including Ramadaan. Even though the 2nd and the 3rd part of Ramadaan are assigned for forgiveness and safety from hell fire it is always due to His Mercy that believers will are forgiven and protected from fire just as He said: (Al Quran 7:156) With my punishment do I afflict whom I will but My Grace overspreads everything - And it is due to this Grace and Mercy that Angels in the Heavens pray for His Mercy 1st, His Forgiveness 2nd and then Safety from the Fire 3rd, for all believers including in the holy month of Ramadaan: (Al Quran 40:07)…"Our Lord, You have encompassed all things in Mercy and knowledge, so Forgive those who have repented and followed Your way and protect them from the punishment of Hellfire" - The angels continue doing this throughout Ramadaan till the last nights including Night of Laylatul Qadr (Night of Power/Destiny) where they descend with Allah's decrees while believer's are asking for mercy, forgiveness and safety from hell fire: (Al Quran 97:4-5) Therein descend the angels and the Ruh (Angel Gabriel) by their Lord's permission with every matter. There is peace until the appearance of dawn.

Prophet Muhammad ﷺ advised making this dua in the last 10 nights of Ramadaan:  Allahumma innaka 'afuwwun tuhibbul 'afwa fa'fu'annee - O Allah, You are The One Who pardons greatly, and You love to pardon, so pardon me.[4] The Purpose in Ramadaan is to attain His forgiveness so we are saved from the Punishment in the Hereafter through His Mercy. Narration from Anas (r.a) and others, states that the Prophet ﷺ climbed up on the Minbar, and then said (Ameen): "It was said 'O Messenger of Allah (saw), why did you say Ameen?" He said: "Jibril (Alaihi Salaam) came to me and said "O Muhammad, he is doomed who sees the month of Ramadaan come and go, and he has not been forgiven." He said, "Say Ameen," so I said "Ameen."[5]

References:
[1] Recorded by Ibn Khuzaymah
[2] Sahih Muslim 1079a - Sunnah.com 
[3] al-Bukhari, an-Nasa'i and Ibn Majah
[4] Jami at-Tirmidhi 3513 - Sunnah.com 
[5] Tafsir Ibn Kathir Volume 5 (Abridged) Shaikh Safiur Rahmaan Al-Mubarakpuri - Darus Salaam