Is it too aggressive for job seekers to send cold-emails to senior?
No, if you have not heard back then there is a reason. It may not be a good reason like your resume didnt have enough key words in it and the candidate management system didnt flag it for further review. That doesnt mean that you should not still get a look at by them so what you need to do is find out who you have in your network that knows someone at the company. Have them make an introduction and see if something can be done that way. Most Senior Managers are so busy that in many cases you will shoot yourself in the foot if you try to skirt the system.