Is it a bad idea to show the interviewer what the normal salary of a job position is from google if they try to lowball you?

Waving data in someone's face is a bad way to negotiate. Accusing them of lowballing you is an even worse way to negotiate. If some kid literally said "you are lowballing me" I'd apologize for the insulting offer and show them the door.

Average salaries you find on the internet are one data point, and quite likely unreliable. Jobs with vastly different compensation/responsibilities can have similar titles, and these "averages" won't know how to differentiate. They do a bad job factoring in different levels of experience and COL in different cities. Anyone making you an offer knows enough about compensation in his industry to rebut your single data point and dismiss your argument out of hand, even if you're right that the offer is below market.

There's a natural information imbalance that favors the hiring company. To negotiate well, you need as much data as possible. The best are anecdotes from people with the role at the company, followed by similar roles at competitors. You want to be as confident as possible about the market rate for your work.

But all of that said, none of that information can force an employer to offer more than he's willing to offer. It can only help you make your case - after which you need to be prepared with how you'll respond to any given offer. Decide in advance what you'll say to each range of offers (for example, i) way below market/expectations, ii) below, iii) at, iv) above, and v) way above market/expectations). Have a decision tree of responses planned. For instance:

i) Our expectations are very far apart. I can't accept that offer. Can you tell me the very best you can do so we don't waste a lot of time? ii) That's below what I was expecting, and all of my research had indicated a market rate closer to X. Is there anything you can do to get me to that figure? iii) I had hoped for X, given my (insert strength here). Is that possible? iv) We're in the range I had expected. My target was just a bit higher. Is it possible to split the difference or are you firm on that number? v) I'm excited to join the team. (don't risk a great offer by overplaying your hand).

For each of the above, you need to consider potential responses and decide in advance how you'll react to each. Preparation is paramount. Ultimately you need to know the lowest number you'll accept before you'll be prepared to walk away so you can put your foot down and follow through if necessary.