This is not legal advice. But I’ve legal b/g.

Truth is before you start an employment and even though you have signed an employment agreement, the company or yourself can choose not to commence with the employment.
This is an anticipatory breach.

If you had provided the company ample notice and the notice is even more than the contractual notice stated in the contract, the principle of mitigation applies. This means the company has to mitigate their loss. They have to use the intervening period to find someone else for the role.

Now let’s look at it from the company’s perspective. Say if the company has hired you but owing to business conditions, the company can tell you they do not want to continue with the employment anymore. Yes even though you have resigned from your job, you would still be expected to mitigate your loss by finding another employment.
Usually even if you sue the company, what they will be required to pay you is damages. The most is equal to the quantum of the notice period during your probation. For the company’s protection notice during probation is usually 2 weeks at most.

Unless you hold a job in the six figures where 2 weeks is probably a lot, it doesn’t make sense to sue once you factor in legal costs.

End of the day, as an employee you tend to have less bargaining power.
You take whatever the company has stated. Even if you force them to honour their obligations when they no longer want to do so, the company will find ways and means to ask you to go. Example, unsatisfactory performance during probation, or make your working condition so unbearable that you’ll leave on your own.
In other words, if the company signal their intention not to commence with the employment even after you’ve signed the employment letter, it’s best to start searching for a new job.