This is not correct. Secular academics disagree quite a lot about the specifics as we lack sufficient historical data but it is very widely accepted that:

* the gospels were written in the 1st century

It is therefore entirely possible that they were written by eyewitnesses, even though many do not think they were written by some of the 12 disciples. The topic of 'eyewitnesses' is however hotly debated. See e.g. https://www.amazon.co.uk/Jesus-Eyewitnesses-Gospels-Eyewitne... which is pro this view but also plenty against.

Even John's gospel, which is often thought of as the latest, may well have been written very early; arguments for a late dating are almost wholly made in relation to the text itself (i.e. it has a 'higher' Christology) and not wider historical data.

Source: I am studying theology at Cambridge University in the UK and have heard several professors here debate these topics, plus I am familiar with the literature.

True, but surely the reason is not that there are no religious believers who have applied rational processes to the question of whether there is a God (or gods) and have concluded that there is - but rather that the scientific method is a method that is only suitable in certain domains.

It's easy to equate 'the scientific method' with any sort of 'rational' evidence based approach, but the term has a specific meaning.

We don't apply the scientific method to solve murder investigations for instance, or to solve math equations. Similarly historians don't use the scientific method to determine what happened in history.

It's not that the choices are the scientific method or ignorance -- it's that the scientific method is not applicable in many of the domains that intellectual religious people have mined to conclude that theism is more likely than atheism. Many Christians point to the historical evidence for Jesus for instance, see (former Prof) Richard Bauchman's 'Jesus and the eyewitnesses' http://www.amazon.com/Jesus-Eyewitnesses-Gospels-Eyewitness-... or Prof Licona's http://www.amazon.com/Resurrection-Jesus-New-Historiographic... 'The resurrection of Jesus - a new historiographical approach' or they have considered philosophical arguments (see what Alvin Plantinga has written for example).

This is not to argue that science and religion are Non-Overlapping MagesteriA (NOMA) as Gould argued, clearly there are overlaps (whether the first humans came in to existence along with the universe 6,000 years ago is a pretty clear example of overlap), but many of the arguments intellectual theists give for thinking theism is more likely are rational, just not scientific.