and welcome to gis.stackexchange!

I agree this is a (simple) CRS mismatching problem:

• Google maps (XYZ tiles) are natively in EPSG:3857 WGS 84 - Pseudo Mercator
• your shapefile data's CRS seems to be EPSG:32627 - WGS 84/UTM zone 27 N

QGIS takes care to reproject on the fly different datasets onto the Project CRS, at least as long as the information it has about the original CRS of each layer is correct.

I would therefore suggest to:

• set the Project CRS to the same as Google Maps, and
• correct the CRS setting of the shapefile

To do so, I would reccomend to:

1. righ-click on GoogleMaps layer in the Layers swatch, then Layer CRS -> Set Layer CRS, then select EPSG:3857
2. righ-click on shapefile layer in the Layers swatch, then Layer CRS -> Set Layer CRS, then select EPSG:32627
3. righ-click on GoogleMaps layer in the Layers swatch again, then Layer CRS -> Set Project CRS From Layer.

you sohuld end up with your Project being in EPSG:3857 (Pseduo Mercator), and the shapefile corectly reprojected onto Google Map's backdrop.

If it is not like that, as a fallback, try starting a new project from scratch, and/or request again to be provided with the actual CRS of the shapefile layer.

By the way, the reason why I suggest to set the Project's CRS like Google Map's CRS is because reprojecting the vector shapefile is computationally much easier for QGIS than reprojecting all Google Maps pixel into another CRS. However, once the two datasets are aligned, you can of course change the Project's CRS to anything you want, and both layers will be happily reprojected.

I agree this seems to be a (simple) CRS mismatching problem:

• Google maps (XYZ tiles) are natively in EPSG:3857 WGS 84 - Pseudo Mercator
• your shapefile data's CRS seems to be EPSG:32627 - WGS 84/UTM zone 27 N

QGIS takes care to reproject on the fly different datasets onto the Project CRS, at least as long as the information it has about the original CRS of each layer is correct.

I would therefore suggest to:

• set the Project CRS to the same as Google Maps, and
• correct the CRS setting of the shapefile

To do so, I would reccomend to:

1. righ-click on GoogleMaps layer in the Layers swatch, then Layer CRS -> Set Layer CRS, then select EPSG:3857
2. righ-click on shapefile layer in the Layers swatch, then Layer CRS -> Set Layer CRS, then select EPSG:32627
3. righ-click on GoogleMaps layer in the Layers swatch again, then Layer CRS -> Set Project CRS From Layer.

you sohuld end up with your Project being in EPSG:3857 (Pseduo Mercator), and the shapefile corectly reprojected onto Google Map's backdrop.

If it is not like that, as a fallback, try starting a new project from scratch, and/or request again to be provided with the actual CRS of the shapefile layer.

By the way, the reason why I suggest to set the Project's CRS like Google Map's CRS is because reprojecting the vector shapefile is computationally much easier for QGIS than reprojecting all Google Maps pixel into another CRS. However, once the two datasets are aligned, you can of course change the Project's CRS to anything you want, and both layers will be happily reprojected.