Yes, it is possible! Home-ownership is not limited to high-income earners. People use various strategies to buy their first home; among them are:
Saving for a one-bedroom unit as a starting place
Buying a home and renting out the second bedroom
Buying a home with a partner
Buying an investment property: a foot in the door, and renting a home to live in
A key element is to manage your finances well, and the best starting point is to record each and every expense you have in a month. This will allow you to identify areas of spending where you can cut back, for example eating out less often, bringing lunch to work rather than buying it, paying off credit cards before they are due, and shopping for cheaper brands.
Once your finances are under control and you are in cash-flow surplus per month, you want to put that excess cash away to save for your deposit. Birthdays and special occasions can be used as opportunities to have financial gifts - to put into saving for your deposit - rather than commercial items that will be used. A deposit for a home may be as little as 5%. As a starting point, it might be worth considering buying a smaller place in a great area, rather than holding out for a larger place in a great area. The capital growth of a smaller home in a great area will out-weigh the interest earned on savings.
At Melissa Maimann Buyer's Agent, I help people from all walks of life purchase their first or next home. Fees are very flexible and reasonable, and you only pay for the service/s that you require, controlling your spend while also ensuring that you benefit from skilled and professional advice.