As a more general answer (not node.js-specific), check eb-engine.log
from your Elastic Beanstalk environment.
Where are the logs? In Elastic Beanstalk's online interface in the sidebar of your environment.
...
2021/06/12 22:40:34.097454 [INFO] app source bundle is zip file ...
2021/06/12 22:40:34.097460 [INFO] extracting /opt/elasticbeanstalk/deployment/app_source_bundle to /var/app/staging/
2021/06/12 22:40:34.097470 [INFO] Running command /bin/sh -c /usr/bin/unzip -q -o /opt/elasticbeanstalk/deployment/app_source_bundle -d /var/app/staging/
2021/06/12 22:40:34.138333 [INFO] finished extracting /opt/elasticbeanstalk/deployment/app_source_bundle to /var/app/staging/ successfully
...
Interpretation:
app_source_bundle
was uploaded to /opt/elasticbeanstalk/deployment/
initially
app_source_bundle
was extracted to /var/app/staging/
If Elastic Beanstalk deployment is successful, you can find the running app's code in /var/app/current
(as Manuel pointed out).