I am not sure if i need to let user see it already eventhough he has not change in the fields. Why on some modal or forms, they already appear? whats the reason behind it? What to save when user has not edited or updated the fields.
I feel the save button helps serve two purposes
1. Reduce confusion
Users are used to seeing a "submit" kind of button at every form. The sudden absence of it, might lead to some confusion. "What happens after I start typing?", "Will it directly start syncing to cloud or something once I type" or "Maybe there's a glitch with this website and it hasn't loaded entirely. In all cases, the user might not be quite sure on what happens next.
Point 1 and 3 of Top 10 Application-Design Mistakes elaborate on this quite well.
2. Creates a perception of control
In continuation of the previous point, a user would feel more in control when they see, well, controls. When a users seeing the "save" button missing might assume an "automatic sync" might be triggered once they start typing. This might make them skeptical about typing at all. However the presence of it, assures they can click it, as and when they feel the forms are appropriately filled.
The Perception of Control is a good read about this. While it does focus more about deception to create a perception of control. It does talk about how important that perception is and how "placebo buttons" can help.
Buttons that do nothing are known as placebo buttons, and they exist everywhere: at crosswalks, in subway stations, and on thermostats. They serve no function, other than to provide the user with the perception that he or she has some control over an automated system.
Technically the save button is a "placebo button" until the user types something into the form.
These buttons already appear to give users a guidance or structure to follow, a simple sequence of form fields to fill out and either to confirm or cancel the input. This is a common pattern to support usability as stated by e.g. Jakob Nielsen (1995, 10 Usability Heuristics for User Interface Design). Rather than messing around with such a well-known pattern you could easily change the visual style of your form, as displayed in the attached image, to keep following the standard and make it more appealing.