As I discussed in an earlier column about establishing your brand at a new job, there are a number of steps you can take to quickly establish among more senior folks who you are and what you bring to the table. One of the best is to ask a key question that you've prepared for in advance in a large division or group meeting. That can be a risk if you ask an obvious or misguided question, but if you do your research and know what the company priorities are, that's how you can begin to get new people to view you as valuable and leave strong impressions with them.
Another possibility is to have your own "conversation tour" where you identify key people you'll be working with and for at your new job and ask to sit down with them to discuss their roles and what they see as important at your company. But you want to frame it as that you're just asking for information to do your job better, not that you're nakedly ambitious, and also have thoughtful responses to establish your brand and value further.
With your boss, too, you want to make it clear that you're simply looking for ways to improve your performance and contribution, rather than pursuing personal goals. Your boss might be wary, but if you begin to show some results that support your boss, and you share or give credit accordingly, then he or she should see your efforts as a plus.
I once worked with a client a software firm who early on in his time there asked a particularly incisive question at a group meeting that really got him noticed by senior managers there. One of them sought him out afterwards and enlisted my client to work on a high-profile project; he later wound up leading the initiative that resulted and has worked his way steadily up the ladder there since.
Remember that in times like these, quickly getting yourself viewed as a player in your company is critical, and there's good ways to do this without antagonizing your boss.