Warning: a philosophical rather than practical answer ahead :-)
The most satisfactory way to implement the splash screen is to wait several years until the HTML people come to their senses and implement the <splash-image> , which can be placed in the <head> section on any page. It will be purely static (no links from it), completely optional, fired with a click or after the expiration date, it will support fade / slide / shatter effects and similar completion effects, it will not require significant efforts so that it does not look like a pop-up window, it will not have a separate URL and will not interfere with search engine robots. This is the best solution to date. But this is simply not an option available to anyone .... else.
Despite Quentin's comment above, approved by several others, I find there are useful contexts for splash screens. Some screensavers are not just “something beautiful” - they may be legitimate content. I found this question while (somewhat fruitlessly) was looking for a way to implement a daily splash screen that could be changed to provide context and emphasis for other website content.
When you look at a huge number of websites that offer dozens of low-value links that fight for the attention of the viewer, 90% of which will never be respected (something even on this terrible site is to blame), it’s easy to imagine that some photos may cost at least thousands of such words. In some cases, this will even add significant value to ensure that such an image is the first that is displayed every time the site is visited.
Of course, if you just want a static surge to make some kind of marketing message enter the minds of your viewers, then please don't - Quentin is right there :-)