Ṣiddīq usually means very truthful, but in this context, it means the one who affirms, i.e., he who does تَصْدِیق. This itself means firm belief and affirmation, so تَصْدِیق refers to faith.

ہُوَ التَّصْدِیْقُ بِمَا جَاءَ بِہٖ مُحَمَّد

Faith is to affirm the religion Prophet Muhammad صَلَّى الـلّٰـهُ عَلَيْهِ وَاٰلِهٖ وَسَلَّم came with.^[1]

تَصْدِیق refers to faith, and the meaning of Ṣiddīq is, “he who affirms.” So, al-Ṣiddīq al-Akbar means, “He who believed and affirmed the religion of the final Prophet صَلَّى الـلّٰـهُ عَلَيْهِ وَاٰلِهٖ وَسَلَّم the most, and who was unparalleled in this matter.”

The one who affirms

The Quran states:

وَ الَّذِیْ جَآءَ بِالصِّدْقِ وَ صَدَّقَ بِهٖۤ اُولٰٓىٕكَ هُمُ الْمُتَّقُوْنَ(۳۳)  

And the one who has brought this truth and those who endorsed him, only these (people) are those who fear (Allah).^[2]

The fourth caliph of Islam, Sayyiduna ꜤAlī b. Abī Ṭālib رَضِىَ الـلّٰـهُ عَـنْهُ said: "‘The one who has brought this truth’ refers to the Prophet صَلَّى الـلّٰـهُ عَلَيْهِ وَاٰلِهٖ وَسَلَّم, and ‘those who endorsed him’ refers to Abū Bakr رَضِىَ الـلّٰـهُ عَـنْهُ.”^[3]

Accepting Islam without hesitation

ꜤAbdullah Tamīmī رَضِىَ الـلّٰـهُ عَـنْهُ reported; the Messenger of Allah صَلَّى الـلّٰـهُ عَلَيْهِ وَاٰلِهٖ وَسَلَّم said, “Whenever I invited people to Islam, they were hesitant