Can I make a claim with my homeowners' insurance if my effective date was a few days ago?

It depends on when the loss occurred or when you noticed it and when the policy went into effect. You can make a claim anytime after you sign the application for insurance and they accept your payment. The question remains what will happen once you file the claim. The State in which you reside will determine what happens after you file the claim. Some states allow Insurance Companies to cancel you without penalty if you have a claim within the first 60-days of a policy's inception date. Ask yourself how bad are the damages to the lower unit and if you can afford to pay for it yourself. This would be a liability claim against you by your neighbor and/or their insurance company. There would be no coverage for your hot water tank replacement but there would be coverage for the damage to your condo or at least to the limited common elements(that part of the condo you are responsible for). Hopefully this was a sudden and accidental water loss because some policy verbiage states..."water damage due to a continuous or repeated seepage of water over a period of weeks, months, years is not covered. Good luck and email me if you need more specific info.