It's as instantaneous as a birth of the flesh, but not as..."loud".
John 3:6-8
6 That which is born of the flesh is flesh; and that which is born of the Spirit is spirit.
7 Marvel not that I said unto thee, Ye must be born again.
8 The wind bloweth where it listeth, and thou hearest the sound thereof, but canst not tell whence it cometh, and whither it goeth: so is every one that is born of the Spirit.
Being born again is being born of the Spirit. As the text above explains, it won't occur as a notable event or display of power, but it will be a change of heart that begins.
John 16:8 [brackets mine]
And when [Holy Spirit] is come, he will reprove the world of sin, and of righteousness, and of judgment:
The Spirit will reprove you and convict you (i.e. you will feel guilty of things you normally didn't have an issue with prior to your conversion, as you begin to love what the Messiah loves and hate what He hates). That's the Holy Spirit's job, causing us godly sorrow and a motivation to do better each day as He teaches us how to love. So if one doesn't experience this inside - or from the Holy Spirit through brethren - one isn't born again.
Important note: Reproving isn't condemnation. Imagine your parent correcting/reprimanding you, but not disowning you. That's the feeling I'm referring to. A perverse generation would have you believe that even reproving is condemnation and thus not of God, but that isn't scriptural and is the reason why so many Christians today - who profess to have the Holy Spirit - continue to act immaturely even after decades in the faith. Don't fall for it. Don't resist the Spirit.
One's new birth begins the process of maturation and sanctification; a work of the Holy Spirit inside as the believer begins your growth "unto the measure of the stature of the fullness of Christ".
Continue to feed your spirit with the scriptures and with prayer, otherwise, like any newborn, your spirit will starve.