The A1502 uses the NVMe protocol but with a proprietary Apple edge connector.
If your plan is to use an NVMe drive with an adapter like in the following thread, you can use a USB3-to-NVMe converter to be able to format the drive before installing it.
You could use something like SuperDuper! to make a bootable clone of your current system on this drive and then install it in your laptop, or you could use your Time Machine method - either will work, though the former will be faster.
This thread is about upgrading MacBook Airs & Macbook Pros (2013-2015) with new high speed and/or high capacity NVMe SSDs. This thread was one of the first to talk about MacBook Pro NVMe SSD upgrades on Macrumors, and was started by user "maxthackray", which we can thank and give tribute for...
forums.macrumors.com
Example USB to NVMe converter:
SSK Aluminum M.2 to USB NVMe SATA SSD Enclosure Reader, Tool-Free USB 3.2 Gen 2 10Gbps NVMe PCI-E 6Gbps SATA M-Key / B+M Key Solid State Drive External Adapter with UASP Trim, for SSDs 2242 2260 2280
www.amazon.com
You could also use an Apple OEM drive as your upgrade, but a USB converter for those is around $130, so it would be cheaper to chain an Apple-to-NVMe converter with an NVMe-to-USB converter.
Example Apple-to-NVME converter:
PCI Express PCI-E 4X M.2 NGFF M-Key to 2013 2014 2015 Apple Macbook SSD Convert Card for A1493 A1502 A1465 A1466 4-lane (x4) PCI Express M.2 NGFF M-Key throughput rates up to 5 Gbps It only support the Macbook SSD to NGFF M-key SSD, It cannot convert to NGFF B-key or B+M key. Please make sure you...
www.amazon.com
I’d recommend the NVMe option, though - Apple OEM drives are really expensive compared to equivalent m.2 NVMe options.