Some improvement can be obtained like this:
- Scale down the image to some realistic size (text 200px high)
Filter > Blur > Gaussian blur(
Size Y=3-4). Make sure that the top of the
odoesn't become too transparent or you'll have a cut there.
Layer > Transparency > Alpha to selection
Select > To Path
At that point you have a path which is a smoothed representation of the text. You just have to "render" it. Since it is a path it can be rendered at any size without losing sharpness.
- Scale the image to required size.
- Add a new layer
Select > From Path
- Bucket-fill selection
For a given piece of text, you can also redo a path manually using the initial layer as a guide, removing all the bumps and shakes in the process. A shape like this would require around 400 anchors(*), so, a long evening for you... and under one hour for someone who's used to the task.
(*) Rendering "welcome" with my usual handwriting fonts yields a path with around 481 anchors, but there are many in the parts of the letters that overlap.
If you have the font, use it in Inkscape. Apply Path > Object to Path to make the written text to vector drawing. If you simply remove the excessive path nodes with the node tool you get smoother curves. By default Inkscape tries to keep the curves as nearly original as possible with less nodes. Prepare to remove tens of nodes per a letter.
Path > Simplify can be tried, but I guess it alters too much. Try it.
If the font doesn't contain the needed simple enough variant you could in theory edit the font in a font editor. That's extremely complex and can cause legal problems if the license doesn't explicitly allow making and distributing new versions. Some font makers prohibit all attempts to make own versions of font files - even if you have paid the font and you are going to use the edited version only by yourself.
Many modern fonts contain finely crafted variants as adjustable or selectable features that can be taken into use in an application program as typographic settings. Unfortunately I do not know is it possible and useful in your case.
Not asked: I would search for a font which has non-crunchy edges by default. There are numerous of them availabe, also free ones.
There is no way to do this perfectly without redrawing it in illustrator, which is a bit of work and not very easy for beginners.
Usually this kind of thing happens when a font is compressed in a jpg or something similar. But in this case the font is "Bombshell Pro by Emily Lime" and the edgyness is part of that font. Maybe use whatthefont to find a similar font like "Forestry Script Regular by Typehill Studio"