"Matěj said he would not come before Wednesday."
Translation:Matěj řekl, že do středy nepřijde.
“he would not come before Wednesday” translates to “nepřijde dříve než ve středu”
“do středy nepřijde” would be “he was not coming till Wednesday”
When given only the English sentence without any context, there's a whole lot of suitable answers.
In English (to my understanding) "would not come before Wednesday" means it's possible he arrives on Wednesday. In the Czech answer, "do středy" usually means including the given day, in this case Wednesday. Better translation here would be "dříve, než ve středu".
This is not ambiguous at all, "would" doesn't mean a possibility here. This is so called reported (indirect) speech. Reported speech shifts tenses, so Tom really meant "will" but here it becomes "would":
Tom said: "I will not come home before Wednesday."
Tom said he would not come home before Wednesday.