You Are Ambitious! I love it!! I feel your excitement. It's great.
You bring up a few different points, so I want to address them one by one.
Unless you are looking at private money or hard money lenders (who make up their own rules), many conventional lenders won't refinance for a cash out until you have held the property for 6 months. Additionally, they would still want to see equity, so getting 100% of your money back in a cash out is slim to none.
In terms of you qualifying for multiple properties, your quickest and most efficient way of doing this is using OPM (other people's money). What I mean by this is using the rent roll to offset your debt to income ratio. After the property has been on your taxes for 2 years (in some cases 1 year), the net income counts toward your overall income. So, when you go to qualify for a new property, you are just qualifying on THAT property, not both. Does that make sense?
A quicker way of doing this would be to purchase a property with tenants already in place. To many lenders, if the property already has a proven track record with tenants, they will allow you to use that income to offset the debt to help you qualify for the property.
Another thing to consider would be putting 20% down instead of 25% down. If timing is your biggest hurdle for building your down payment up, then it may be worth the slight interest rate bump you will see from slightly lessening your down payment.
Lastly, I would recommend HEAVILY, that if this is your first experience with real estate investing, you slow down just a beat and allow yourself to learn about being a property owner and manager before jumping in to several properties that teach you the lesson in an extreme way. You may find, after your first one, that you don't like the type of property you purchased, or the price point, or the area. If that's the case, it's alot easier to recover from 1 property versus 5 or 7 or however many that came too quickly after that first 1.