Could an immediate field goal be advantageous in NFL?

In general, no, this would not be a good strategy.

First, it would be a signal that you do not trust your offense. Doing this would be admitting that you believe that your offense has a low likelihood of scoring and a high likelihood of a turnover.

Second, as soon as you kick the field goal, you are giving the ball to the other team. The result of this would be minimizing your own team’s time of possession. This gives the opponent more opportunity to score.

A field goal is worth less than half of a touchdown. By never going for a touchdown, you are saying that you believe that every possession you have will end in a turnover. If even half of your possessions do not end in a turnover, then you should not settle for a field goal before you are forced to.

The average number of offensive drives for an NFL team is around 12, and the average number of turnovers is around 2.6, so it would be a mistake to artificially end every drive early and avoid touchdowns just to minimize turnovers.

Definitely not.

A team which gets a first down with 40 yards to go can expect to score around 2.5 points (source: the graph at the bottom of Advanced Football Analytics).

A ball spotted on the 40 yard line will result in a 57 yard field goal attempt. A 55 yard field goal attempt has a success rate of around 50% (source: Field Goal Success Probabilities by Direction), dropping rapidly from there. That gives a maximum expected points of less than 1.5.

There are probably some second order effects here around things like where the opposing team starts their drive, but they're not going to make up a full point of difference.

Definitely not at the 40, because of how hard a field goal at the 40 is (edit: see Philip's answer for that calculation, I'll not duplicate that here). I will say that the graph in that answer is a bit old, 2014, and unfortuantely that site isn't updated anymore, but it's still close enough for that answer to be right.

See the JAX-MIA game from 9/24/2020 for a good example; here, there is a 1st and 10 on the 48, EPB (Expected Points Before the play) of 2.3, and a 2nd and 5 on the 43, EPB 2.5. Then the following first and 10 on the 37 has an EPB of 3.1; that's above the value for a field goal even if it had a 100% chance of making it. Of course, the Dolphins scored a touchdown on that drive, but it's the right call to press on whether that succeeded or not.

For a bit of detail over Expected Points, you can read this older ESPN article; but in short, expected points are the number of points that are statistically predicted to be scored from that down and distance from the average team - not from a specific team, so the Chiefs probably score a bit more than the Bears from a particular yard line; it's not perfect, but it's decent.

This can be used to make decisions; such as, on 4th and 1, do I go for it, or kick a field goal / punt? If the expected points from a particular down and distance is greater than three, then it's probably better to go for it on average than it is to kick the (3 points or less) field goal, or punt; but in the latter case, you need to take into account the expected points for your opponents starting on that line also. Again, it's not perfect (as it's not team specific), but it's a good metric and as good of one as we have.

The other consideration I would suggest, beyond the pure numbers, is that defenses tend to tire out more easily than offenses. As such, you're better off forcing their defense to stay on the field longer. The NFL is unique in having players only play one side of the ball, and that makes this a much bigger concern than in other sports.

I assume you mean "Attempt a field goal on the first down". Attempting a field goal on the fourth down is common practice.

As other posters have pointed out, there are close to even odds on making at field goal at 40 yards. Getting closer increases the chances of making the field goal, but it also means that a touch down would have been easier as well.

Missing at your opponent's 40 yard line not only gives up a possible touchdown, but hands the ball over at your opponent's 40 yard line. Even if you don't get a first down, every yard you can advance the ball not only makes a field goal attempt more likely, but makes the field position if you miss worse for your opponent.

Here's one set of turnover stats:

https://www.sharpfootballstats.com/ytd-turnover-rates.html

There are rates as low as 0.0%, and assuming that 0.05% would be rounded up to 0.1%, that means that there are plays with turnover rates no higher than 0.04%. At that rate, there would be on average one turnover in every 2500 plays. Even the average play wouldn't be better than making a field goal attempt, it still would make sense to use up all your downs with safe plays that move the ball down the field before making the attempt.

If they changed the rules so that a team that misses a two point conversion attempt can still make an attempt at kicking it in for an extra point, as long as there wasn't a turnover on the two point attempt, how often do you think teams wouldn't start out with the two point attempt?