Depends on which product level you want for calculating NDVI. Level-2 is atmospherically corrected (Surface Reflectance) Landsat data, whereas, Level-1 is not. If you want Level-2 based Landsat NDVI product, you can order it directly from https://espa.cr.usgs.gov/ordering/new/ using the specific Landsat scene Product ID.
That is perfectly fine. In fact, it is encouraged to perform atmospheric correction of Level-1 Landsat data manually. You can then compare your results with USGS provided Level-2 based NDVI product. Probably there would be some differences depending on which atmospheric algorithm you use. Here is an article that compares multiple atmospheric correction algorithms Article Evaluation of atmospheric correction models and Landsat surf...
Natalia de Souza that is correct, you can download the Level -2 SR bands and convert the valid range by using the rescaling factors as described in the Landsat 8 product guide Table 6-1 on page 10. You can download the product guide from here https://www.usgs.gov/media/files/land-surface-reflectance-code-lasrc-product-guide
Once you get the SR NIR and Red bands in the 0 to 1 range after rescaling, you can use the NDVI formula to get the desired -1 to 1 ideal NDVI range.
I think there is a similar product guide for other Landsat series, just search for it on the USGS website. You might also benefit from a similar discussion on the topic that I've attached here.