In a NT passage that speaks directly about an actual service in a local church, Paul declares the following:
1Co 14:23 If therefore the whole church be come together into one place, and all speak with tongues, and there come in those that are unlearned, or unbelievers, will they not say that ye are mad?
24 But if all prophesy, and there come in one that believeth not, or one unlearned, he is convinced of all, he is judged of all:
25 And thus are the secrets of his heart made manifest; and so falling down on his face he will worship God, and report that God is in you of a truth.
This text speaks of an unbeliever who comes into the midst of a whole church that has gathered together into one place and everyone prophesies with the result that the unbeliever comes under genuine conviction and is brought to worship God openly in their midst.
Because this divine revelation plainly speaks of God’s using the combined ministry of an assembled local church to bring an unbeliever to worship Him, we have biblical warrant for inviting people to come to church with us so that they are put in the position of having God work in their hearts in the manner spoken of in this passage.
Whether God chooses to work in such a manner in any given service is not our responsibility—our part is to put them in the position for Him to do so, should He see fit to do so.
Christians should invite unbelievers to come to church with them.