Chaitra Navaratri starts with pAdyami (1st day) of Chaitra month/mAsa.
King Dasaratha wanted to coronate Sri Rama in chaitra month.
चैत्रः श्रीमानयं मासः पुण्यः पुष्पितकाननः | यौवराज्याय रामस्य
सर्वमेवोपकल्प्यताम् || २-३-४ राज्ञस्तूपरते वाक्ये जनघोषो महानभूत् |
"This is the glorious and auspicious month of Chaitra, in which the
forests bloom with flowers. Let all arrangements be made for the
coronation of Rama as prince." While these words of the king were
being completed, there was a great delightful uproar of the people.
It was described in Srimad Ramayana that Sri Rama reached the hermitage of the sage Bharadwaja, after exile period, on the fifth (5th) day of lunar month after completion of 14 years of exile.
पूर्णे चतुर्दशे वर्षे पञ्चम्यां लक्ष्मणाग्रजः | भरद्वाजाश्रमं प्राप्य
ववन्दे नियतो मुनिम् || ६-१२४-१
After completion of fourteen years of his exile and on the fifth day of the bright half of the lunar month , Rama, who was disciplined
even now, reaching the hermitage of the sage Bharadwaja, offered his
salutation to the sage.
So Sri Rama's coronation did not take place on the 1st day of Chaitra.