First: Chicken vs. Egg
Allay your project manager's fears about "choosing the wrong persona" by explaining that the data & market research should do that for you.
Personas reflect the target market because they should be derived from actual research data (surveys, market & competitor analysis, etc) or at least educated assumptions about who you think potential customers might be. They don't define your audience - they put a face on the stats to help you focus on narrower brackets already defined.
Even if you don't have hard data yet, somebody must have some idea what problem you're trying to solve & for whom, which can point the personas in an initial direction (if nobody can answer that basic question & you're already working on the product, bewwaaaare! :P).
Second: Once Upon a Time
Personas aren't set in stone - they exist to help you tell a story and narrow your focus from "everyone in the world" (which is untestable and unmanageable) to progressively improved results you can test and validate. They should be a living composite synthesized from multiple real input sources. Adjust their stories regularly to reflect your latest prototyping results & revised assumptions.
Maybe persona #1 "Lisa Hernandez" starts out as a single career woman who needs a product to do X, but [based on user surveys, prototyping, etc] later becomes a married teleworker who wants a product to do Y and Z. Her story is no different from a book or movie skipping around in time to reflect new circumstances.
Third: Lisa needs your help
Personas also offer a way for your team to empathize on a personal level and connect with the goals they're working toward. Solving a problem for a real (fake) face/name/person, can boost your team's motivation, creativity, and focus, instead of getting bored by anonymous data & statistics.
No Persona: "Our budget software is aimed at every student loan holder on the planet. It will let them pay their bills from their phone. Marketing says it should be gamified and social. Accounting says it needs to cost $10.99 to make a profit, but we're looking into ads as well."
With Persona: "Lisa Hernandez graduated from State U last year with $40K in debt and a job in sales at $15/hr. She wants help paying down her student loans each month, but she hates spreadsheets and would prefer a fun, convenient budgeting app. She likes challenging her friends to social games, so think of how to use those avenues to keep her motivated and using the app regularly. We'll test a paid version at $10.99 for pro users, but we're looking at an ad-supported version so it doesn't cost Lisa or her friends anything directly."
... Which project would you rather work on?