The ¿ and ¡ prepare the reader mentally for what’s coming and let the speaker adapt pronunciation.

Consider the following 2 sentences in English:

It’s raining.

and

It’s raining?

Meaning and intonation are different. Luckily our eyes don’t read strictly in one direction like a scanner but instead they skip back and forth a lot (saccades) which means your brain registers the question mark even before you get to pronounce the first word.

So why no extra dot at the beginning? Because it’s the default case. And since the function of the dot is to separate sentences a single one already does the job. Note how there is also no double period when a sentence ends with an abbreviation or abbr. And in headers it’s often fully omitted because the layout itself signals the separation from what precedes or follows.