The four gospels, the book of Acts and the epistles by the apostle Paul affirm very clearly that the early Church was endued with power from on high. Christians during the apostolic age had access to all the supernatural gifts of the Spirit and were able to perform signs and wonders to confirm the message of salvation they were preaching.
What are the strongest apologetic arguments for believing all this? Are there sufficient reasons to believe that the apostles and the early Christians in general had access to supernatural power from the Holy Spirit to perform miracles, signs and wonders and to operate in the supernatural gifts of the Spirit?
Are the anecdotes recorded in the New Testament reliable (and if so, according to what standard)? Is there any corroboratory extra-biblical evidence? I'm open to any kinds of lines of reasoning and evidence giving credence to the scriptural accounts of miracles in the early Church.
Another way to put it: how can we convince a skeptic that supernatural things happened during the apostolic age, or at least that it is not unreasonable to believe that they did?
Answering questions in the comments
Q. What in your opinion is the difference between 'apologetic arguments' and 'arguments' in general?
A. By asking for 'apologetic arguments' I'm basically expecting arguments that people would present if they were in a formal debate as an apologist against a skeptic and they had to make a case for their belief, in front of an audience. If a dedicated Christian apologist has already addressed this specific question, citing their arguments would be highly encouraged and appreciated as well.