As far as I can tell there was no indication that the Union was planning the first strike, deciding instead to wait until after Fort Sumter had been fired upon to begin military movements.
What was Lincoln's reasoning behind this rationale? The Constitution makes it very clear that secession (which the Confederates had already demanded) authorizes the federal government to “suppress insurrections" (Article 1, Sec. 8).
I'm not aware of how militarily advantageous Fort Sumter was at the time. It does seem strange, however, that Lincoln would essentially hand off ownership of it to the enemy to claim "justification" for something he/Congress was already authorized to do.
The short answer: political and practical concerns. The Civil War was a highly politicized war, and forcibly relieving Fort Sumter (the only reasonable military action to take at the time) would have had harsh political consequences, including pushing states towards secession. And speaking of reasonable military actions, the U.S. army was in no position for a meaningful attack on seceding states, even if it was politically workable.
One of the things that made Lincoln a great leader was his strong awareness of the political ramifications of military actions. Occasionally this led to boondoggles (e.g. the constant requests to generals to aid Unionists in East Tennessee), but it also led to the adroit handling of situations like the Sumter Crisis.
By the time Lincoln took office on March 4, 1861, seven states had seceded - SC, GA, AL, MS, LA, TX, FL. There were still eight slaveholding states that had yet to secede - VA, NC, TN, KY, MO, AR, MD, DE. Lincoln was keen to have as few states secede as possible, whereas an armed relief of Fort Sumter would have pushed those wavering states over the brink. Instead, Lincoln was able to force the Confederate bombardment without himself threatening the use of force, one of his first great feats of political maneuvering.
Ultimately, four of those eight remaining states ended up seceding in response to Lincoln's call for volunteer soldiers. But Lincoln had still won a very significant political victory - namely, moral high ground over the Confederacy that bolstered morale at home, undercut the Confederate political narrative, and possibly gave the Union an edge in international negotiations.
Second, as mentioned, was the fact that Lincoln called for volunteer troops in the immediate aftermath of Fort Sumter. His call for 75,000 troops was five times the current size of the U.S. Army, most of which was stationed along the Western frontier and far away from the seceding states (except maybe Texas). On top of that, even by the time of First Bull Run, the U.S. Army was a long way from the levels of organization, mobilization, and discipline that would characterize it by 1862. So large-scale military action in Spring 1861 would have been unwise even if practicable - really, both the United States and the Confederacy were starting from similar places in terms of land forces, and Lincoln's rapid mobilization was indeed met tit-for-tat by the Confederacy. This would have been as true before Fort Sumter as it was after.
Further reading: