If anyone is interested in doing this without code injection, you can hard-code them in the custom CSS as follows:
/* Sets up an animation to fade your captions in */
@keyframes fadeIn {
0% {opacity: 0;}
100% {opacity: 1;}
}
/* makes the captions centered */
.gallery-grid-wrapper .gallery-grid-item {
text-align: center;
}
/* Styling for all the captions */
.gallery-grid-wrapper .gallery-grid-item:after {
display: block;
font-size: 80%;
margin-top: .5em;
opacity: 0;
animation: 1s ease-out 1.5s 1 forwards fadeIn;
}
/* These are the captions for each gallery item */
.gallery-grid-wrapper .gallery-grid-item:nth-child(1):after {
content: "Caption for the first gallery item";
}
.gallery-grid-wrapper .gallery-grid-item:nth-child(2):after {
content: "Caption for the second gallery item";
}
.gallery-grid-wrapper .gallery-grid-item:nth-child(3):after {
content: "Caption for the third gallery item";
}