Permitting for Mining Needs Act of 2023 This bill expedites the review of mining projects on federal lands and limits judicial review of mining projects. For example, the bill expands the federal permitting and review processes under the Infrastructure Investment and Jobs Act for critical minerals. Under the act, the Bureau of Land Management (BLM) and the U.S. Forest Service, to the maximum extent practicable, must complete the federal permitting and review processes related to critical mineral mines on federal lands with maximum efficiency and effectiveness. This bill expands this process to include all minerals as defined by the bill, not only critical minerals. The bill also establishes deadlines for completing the review of mining projects under the National Environmental Policy Act of 1969. In addition, the bill also expands the meaning of covered projects under the Fixing America's Surface Transportation (FAST) Act to include (1) certain mineral production projects, and (2) certain actions taken by the Department of Defense. Such projects qualify for expedited environmental review. It also establishes requirements to expedite the review or authorization of certain mineral projects, such as (1) mineral exploration activities with a surface disturbance of no more than five acres of public lands, (2) ancillary mining activities, and (3) uranium projects. Finally, the bill limits judicial review of a permit, license, or approval issued by a lead agency for a mining project by requiring the filing of claims within a certain time period.