I have clients that are buying homes or renting a new home. Some of them are or are going to be landlords, others are first time home buyers, just moving closer to work, or getting a change of scenery.
One thing they all need to have is insurance. The lender will require it. If you are paying cash for a property, you really need to insure it right away to protect your investment.
The question is timing. Here in California, for example, we have escrow. That means that the paperwork and money go through a neutral third party which then sees that title to the property is switched over and sent to the county recorder for recording, money is disbursed to the appropriate folks, loan is funded, and much more. They also often make sure that insurance is in place on the property as a condition of the loan or they may recommend that a cash buyer get insurance at or a little before the close of escrow.
The date you close escrow, or take possession of the property, is the date you own it. Lenders will often request insurance shortly before the close of escrow so that they have proof that the property is insured when the loan documents go back to underwriting. This way the lender can review everything at once and give the ok for the transfer of funds from them and escrow can close.
Often, the closing date changes due to various circumstances. Sometimes it closes earlier, sometimes later. Your insurance agent must be made aware of these changes. The lender will need an updated proof of insurance to reflect the new dates. If you are paying cash or renting, you will want to make sure you have insurance before you move anything in. People have had possession's stolen from their homes when they are moving in or moving out.
Remember, a little communication with your insurance agent can save a lot of frustration and time.