It usually takes about two weeks for new music to reach Spotify, so April 5th might be cutting it close but there is a chance it will make it. If you wanted to be safe, I would move the date back until April 10th to be sure it reaches all platforms at the same time.

How long does Spotify approval take?

Every partner site should process your music within 1-4 weeks. All of our partners do honor release dates and will not make a project available to the public until the date you select, as long as they have enough time to process your release.

How long does it take for Spotify to download songs?

(usually it takes about 4-5 min on 4G to download a playlist with about 200-300 songs on normal quality with an average song time 4-5 min). You can change the quality in Settings > Music Quality > Download. Higher the quality, slower the download, higher the space it takes on your device.