Idiom meaning inferring too much from the available evidence

Jumping to conclusions

Jumping to conclusions ... is ... where one "judges or decides something without having all the facts; to reach unwarranted conclusions".

[Wikipedia]

Jump to conclusions

To make decisions or form opinions before one has all the pertinent facts.

• I know you found some suspicious things in her office, but don't jump to conclusions—talk to her first.

[Farlex Dictionary of Idioms]

Read too much into something

to think of (something, such as a comment or situation) as having a meaning or importance that does not seem likely or reasonable

In a case like this I think I'd say:

You put (or added) two and two together, and got five.

https://dictionary.cambridge.org/dictionary/english/put-two-and-two-together-and-make-five

Although this expression does suggest that the inference is wrong, rather than only unjustified.

Both the aforementioned "reading too much into something" and "jumping to conclusions" are good idiomatic expressions for the meaning sought by the OP.

"Jumping to conclusions" can be expressed less idiomatically and more formally as "faulty generalization". The Wikipedia page cited currently includes some eleven different versions of this, all more or less formal, with the most idiomatic being "leaping to conclusions" and "secundum quid" (where the idiom in question is Latin).

There is also the rather idiomatic expression "making a mountain out of a molehill". This is more typically used to indicate when someone is exaggerating the importance or impact of a small problem, but it can be and is used on occasion to refer to what the OP asks about, drawing too many conclusions from too little evidence.