Yes, government should be capitalized if it comes at the beginning of the sentence, if it’s attached to a specific country, if it’s a part of title and if it comes as part of a question. It also can’t be capitalized, if it comes as a common noun and not refers to specific government.
The Government of Egypt ( attached to specific country).
What forces the Government not to avoid the problem ( Title).
What will the Government do to face this financial problem?
the government in Egypt took serious steps to solve the problem. (common noun).