If you're wanting an example of the way an invitation is given today in churches from the NT, you will not find it...
The main reason? There were no church buildings in the NT. No aisles to walk down. No pews to set in. They met in homes... it was more personal. Oh and most people were saved outside the meetings, not in them. why?
Well put yourself in their shoes. A sinner could have "ratted you out" if they did not accept Christ as Savior. They could have went to the authorities and told them about your little "cult" And you could have been killed.
So anyone they brought into the worship service, they made sure was already a Christian. So why would there have been an invitation, if they already knew everyone there was saved?
But times changed, and church buildings were built, and pews were brought in, and people got comfortable, and forgot where they came from. And got lazy. No longer do we go to the streets for converts, we wait in our pews for them to come to us.
Is an invitation wrong just because it is not commanded in the NT to be given? No more than the other things we do on a Sunday morning that are not mentioned in the NT. Bulletins, choirs, Microphones, pulpits, the altar, indoor plumbing, musical instruments, a prelude, postlude, doxology, Sunday School, birthdays, anniversaries, announcements, etc. are not mentioned, but are used for God.